The Grasshopper Experiment - S1-E8
Corrected entry: Leonard wonders aloud "I wonder who's going to tell his (Sheldon's) parents they're not having grandchildren." Leonard and Sheldon have been sharing the apartment for long enough for Leonard to know that Sheldon's father has been dead for a number of years, but it is at least since S1E04, when Sheldon's mother says "God rest his soul" while talking about his father.
The Hawking Excitation - S5-E21
Corrected entry: Stephen Hawking tells Sheldon he made an arithmetic mistake on page 2 of his paper. Sheldon then quickly turns pages on his paper to find the error, but Sheldon turns several pages of his paper, way past the second page, and still finds the error Stephen had noted.
Correction: Scientific papers number their pages differently to how one would assume. There are pages before page 1 begins which are often numbered using Roman numerals. Therefore Sheldon is correct in turning several pages to find page 2.
The Locomotive Manipulation - S7-E15
Corrected entry: Sheldon asks whether the train carriage has "link-and-pin" type couplers, when he would know that such couplers were outlawed by the Safety Appliance Act of 1893.
Correction: It would easy for Sheldon to ignore this fact when he is aboard a train that has been restored to its original design; internally and externally. He has been building toy models since he was a kid. He just wanted to know to what level this train has been restored.
Corrected entry: At the end of this episode when Penny asks to use Leonard and Sheldon's bathroom for a shower, when she goes down the hallway towards the bathroom/bedrooms, she turns past the bathroom (the door that is visible from the living room) and turns right and goes towards the bedrooms.
Correction: Penny could simply be going to grab a towel from the linen closet before having her shower.
The Bat Jar Conjecture - S1-E13
Corrected entry: When the guys are practising for the Physics Bowl and they are sitting across from Penny, Leonard is sitting in Sheldon's seat, which Sheldon would never allow.
Correction: In most cases, this would be true. But given the way things were set up, he had to pick a new, temporary spot for the practice. It's likely that their living room setup is too complex to change just for a short amount of time, which is why the practice area was set up as it was. Sheldon chose a spot related to the practice area so he would be comfortable, just like he chose a new spot when the gang went to the north pole.
The Roommate Transmogrification - S4-E24
Corrected entry: Bernadette tells Howard that she chose the premature ejaculation project because neither of them has any heart diseases. However Howard has stated more than once that he has transient idiopathic arrhythmia. Also in the previous episode he actually emphasizes that his family has a history of heart diseases and alludes to a cave painting showing one of his ancestors clutching their chest.
Correction: Transient idiopathic arrhythmia is not a disease, it is a disorder. They are different things.
The Justice League Recombination - S4-E11
Corrected entry: At the end of the episode, when Sheldon imagines going to the Grand Canyon to scream about Leonard, that's not the Grand Canyon, signs not withstanding. The location is Dead Horse Point State Park in Utah (near the town of Moab), with the view looking roughly south into Canyonlands National Park. [GPS near 38°28'12" by 109°44'30".] It's several hundred miles upriver from the Grand Canyon. [At least it is along the Colorado River.] The first national park sign looks authentic, but the small one at the overlook is fake, since that's not the Grand Canyon. And by the way, since it's just after New Year's, there would likely be snow at both the Grand Canyon and Dead Horse Point; the images used are not winter scenes.
Correction: But it's all occurring in Sheldon's mind. He does have an eidetic memory, but if he has never been to the Grand Canyon he can't remember it. He's imagining what it would look like if he were there.
The Nerdvana Annihilation - S1-E14
Corrected entry: At the beginning, when Leonard has won the online auction, we see a shot of his laptop computer screen showing an Apple Safari browser window with Mac OS X window controls, but the laptop is a PC, not made by Apple. Mac OS X can only run on Mac hardware.
Corrected entry: Penny uses different mailboxes along the top row to get her mail.
Correction: My mailbox was changed three times in the three years I lived in my last apartment.
Corrected entry: Leonard and Sheldon live in 4A and Penny in 4B. Yet when they go to the mailbox downstairs, Sheldon's mailbox is the upper left one while Penny's is the third or fourth one from the left. Mail boxes have to be in apartment order, not necessarily for the tenant who could remember where their box is but for the mailman to be able to use the apartment number as to placement of the mailbox. Whenever a sub carrier would do the route, he wouldn't be able to follow the random pattern.
Correction: My first apartment building didn't have them in order. The boxes were marked with either the apartment number, the tenant names, or both.
The Shiny Trinket Maneuver - S5-E12
Corrected entry: In 3-14 "The Einstein Approximation" Bernadette stated that she is able to easily handle children as her Mother ran an illegal day care centre in their basement. However, in this episode she states that she hates children because her mother worked and she had to bring up her siblings, and she cannot properly react to children. So which is it? Can't be both.
Correction: In 3-14 she says she can handle "stubborn children" and in 5-12 she refers to "little kids". Every parent will tell you there is a big difference in behavior in children at child-care age [i. e. Daycare children] and little kids [a little older]. It is easier to get them to do things when they are small but once they develop their "attitudes", it is very hard to get them to do what you want.
Corrected entry: When Howard is showing Penny the online game and Penny expresses interest, Raj says "Smooth", even though Penny is right there - breaking his mutism rule.
Correction: This has never been a diagnosed condition in his case. In Episode 13 of the same season, during a group conversation he accidentally says "good story" with Penny present and immediately realized that he talked in front of a female then covered his mouth. This is just a individual non-medical problem.
The Financial Permeability - S2-E14
Corrected entry: In 'Pilot' (season 1, episode 1), Leonard and Sheldon attempt to sell their sperm for money to install a T1 line in their apartment, and in 'The Dumpling Paradox' (season 1, episode 7), Sheldon says to Leonard "Frankly, if I could afford the rent, I would ask you to leave". Yet in this episode he says to Penny, "My expenses account for 46.9% of my after-tax income". The only way that his expenses could account for less than half his income just over a year after these lines can only really be explained away if the university gave him a pay rise of over 100%, which is incredibly unlikely for many reasons.
Correction: There are so many possible situations that could explain all of this. Regarding his payrise, You said "unlikely" but that does not mean impossible. That aside, Sheldon could have changed his spending/expense habits. Personally, I did when I got a payrise, regardless of how much it was. Also Sheldon has also proven to us that he is capable of making sarcastic comments now and then whether he is aware he is doing it or not.
Corrected entry: In "The Loobenfield Decay" Sheldon and Leonard go to absurd lengths to avoid having to hear Penny perform because her singing voice is so horrible. But in series 2 episode 18 "The Work Song Nanocluster", series 3 episode 3 "The Gothowitz Deviation" and series 3 episode 8 "The Adhesive Duck Deficiency" (amongst others) she is shown to have a strong, pleasant singing voice, and she sings in front of both men without them objecting. They aren't just being polite - they genuinely like her singing. So, which is it?
Correction: If either of those episodes occurred before "The Loobenfield Decay" episode than this could be a valid plot hole BUT they all occur after. It is fair to conclude that she got better.
The Luminous Fish Effect - S1-E4
Corrected entry: When Penny and Sheldon are driving to the supermarket, Sheldon is explaining the weight of the car and how it affects her braking time. He estimates the car's weight to be 4000 pounds, 140 for himself and 120 for Penny, and then rounds the total up to be 4400 pounds, when it actually should be 4260. It's extremely out of character for somebody like Sheldon to make such a basic addition mistake.
Correction: Or he could be including other things he just failed to mention, such as the contents of the vehicle and trunk.
The Friendship Algorithm - S2-E13
Corrected entry: Sheldon asks at the book store information desk if they have any books about making friends, and the employee tells him that all their books like that are for "little kids." It is unreasonable that the employee would not have been able to tell Sheldon about the very well known self-help book "How to Win Friends and Influence People," if Sheldon had not already been able to discover it through a cursory internet search.
The Hamburger Postulate - S1-E5
Corrected entry: When Leonard is explaining his thoughts to Sheldon, during the rant which includes him naming who he intends with the words she or her (eg "She: Penny, Her: Leslie), he states, "Indicating that She: Penny had no interest in me asking Her: Penny out," which makes no sense. (00:03:40)
Correction: Lenord is confused and ranting so making a mistake in that situation is not unlikely.
The Confirmation Polarization - S12-E13
Corrected entry: Sheldon meets two new fellow scientists, one of which is Sean Astin, who played Sam Gee wise in the Lord of the Rings. Surely, Sheldon would know who he is.
Correction: Suspension of disbelief has to play a part here. Actors are allowed to play other roles, and being many years later, Sean Astin looks quite different, so even if there was a meta element of "this person looks like the actor who played Sam", Sheldon wouldn't necessarily even notice the similarity.
Correction: I'm not sure if this is meant to be a troll entry or a joke. Sean Astin doesn't play himself in this episode, he plays Dr. Pemberton.
The Habitation Configuration - S6-E7
Corrected entry: Howard states in The Shiny Trinket Maneuver that he started doing magic to try to get girls to come to his room, but in this episode he tells her he started magic when his Dad left because it made his Mom happy and made her forget for a while.
Correction: He also may have gotten the idea for doing magic to get girls to his room, but actually started doing it to cheer up his mother.
The Boyfriend Complexity - S4-E9
Corrected entry: Penny's father says, "I want grand kids before I die, and I want them to grow up in a house without wheels," but in season 2, E20, Penny asks Leonard to buy a comic book for her 13 year old nephew. Her nephew would be her father's grandson.
Correction: Her mother may have had a child with another man before marrying her father, which would make the nephew a step-grandson and not a "real" one in her father's eyes.
Correction: Episode S01E04 ended with Sheldon asking his mother if Dr. Gablehouser is going to be his new daddy and her saying "We'll see." So he could be the other "parent." Or his mother could have met someone else between the episodes.
Captain Defenestrator