Plot hole: Cat wasn't manufactured by the Jupiter Mining Corporation and had no connection with them, being born three million years or so after they lost control of Red Dwarf. The takeover by M-Corp would mean nothing to him. Why, then, does he become invisible to Lister?
Continuity mistake: In the episode "First Kiss," Justin has a girlfriend, Miranda. But in this episode Justin starts dating this new girl from his class, who's actually the same Miranda. This doesn't make any sense. How is she a new student and how could they just meet if they were dating eight episodes ago?
Factual error: Throughout the whole show Godber, 'Bunny' Warren, McLaren, the Prison Governor and many of the guards refer to Fletcher as a Cockney. He even identifies himself as a Cockney on a number of occasions. However, in several episodes he refers to his upbringing in Muswell Hill and in this episode he refers to his having been born there - and we see his old stamping ground in that episode when he gets a weekend's compassionate leave. Nobody from Muswell Hill would ever refer to himself as a Cockney - Muswell Hill isn't even in East London!
Revealing mistake: While Andy, Aunt Bee, and Opie are at the Hollywood studio watching a scene being filmed, when Andy mistakenly stands up and interrupts the filming we can see the wall and shelves behind the director, and it should look familiar because it's the wall and shelves from Floyd's shop in Mayberry.
Factual error: There is not a snowball's chance of Howard becoming an astronaut. He suffers from cardiac arrhythmia, something about which he is completely open. "Transient" or not this is easily detectable by a simple electrocardiogram, which is a fundamental part of the many medical examinations a potential astronaut will have to pass. He wouldn't even be allowed to start basic training. Note also that during his basic training he shows signs of severe stress and trauma which would inevitably trigger a cardiac episode. Even if it didn't the fact that he was falling apart at the seams would have him removed from the programme for his own good.
Continuity mistake: Lily and Marshall mention that they've been using the same toothbrush ever since they've been together, but in the 14th episode of the 1st season, "Zip, Zip, Zip", Marshall and Lily are simultaneously brushing their teeth with a tooth brush each (before Ted and Victoria get home). (00:05:05)
Plot hole: When teenage Prue has run away with the demon, and Phoebe and Piper find her in the park, teenage Prue is 'killed'. Her sisters drive her home to get Leo to heal her, but shouldn't they have just been able to call to Leo to orb to them when Prue was first hurt, and heal her in the park, and save driving back to the Manor and risk Prue dying?
Revealing mistake: In the scene in the coffee house, Phoebe is talking to Monica who is drinking a cup of coffee. Towards the end of the scene, the camera is on Phoebe who is smiling & laughing at Monica. In the right hand corner is a side view of 'Monica' however, it is not Courtney Cox in the scene, but a completely different actress. [Widescreen version only, although the "wrong" nose is visible in the original]. (00:06:20)
Continuity mistake: In episode 10 (Joey's Place) the Tanner family move Joey into the garage, redecorating it so the entire place is filled with Joey's furniture, but in this episode it shows the characters in and out of the garage which is completely empty and back the way it was before Joey moved in. Later in the episode Joey's stuff is out of the alcove again.
Continuity mistake: In 3-7 "Employee of the Month", Joe Christie says he was with Monk when he got the news of Trudy's death. He said Monk had been laughing, and that he never heard him laugh again. In this episode Monk and Stottlemeyer get called to the scene of a crime, a women's clinic. In this episode there is a flashback to the exact same location years earlier and to Stottlemeyer getting the phone call about Trudy's death. He and Monk were working a case that day and Joe Christie was not present.