Character mistake: When Walt and Gretchen are talking about the elements in the body, they list hydrogen, oxygen, carbon, nitrogen, calcium, iron, sodium, and phosphorus. The percentage is short and she says "supposedly that's everything." But they don't count elements like sulfur (which has a greater abundance than sodium), potassium, chlorine, and magnesium. Even as college students, they would know those elements are in the body.
Character mistake: When Walt steals the bottles of "hydrofluoric acid," they are misspelled on the labels as "hydroflouric." This misspelling is corrected when hydrofluoric acid reappears in season 4. This was corrected for some DVD releases but is still visible on some streaming services. (00:11:20)
Character mistake: When Walt is in the bathroom using hydrogen peroxide to clean his leg wound he received from killing Crazy 8, he notices blood on his pants. He tries to clean the bloodstain off with a toothbrush. I think that any and EVERY chemist would know that hydrogen peroxide almost instantly removes blood stains from clothing. But, instead of using this somewhat common knowledge, Walt scrubs the stain with a toothbrush under the sink. Even if he had never heard of this 'trick', given the nature of H2O2 and Walt's understanding of chemistry, he would have realized this chemical solution immediately... Especially since he used the peroxide seconds before discovering the blood stain. (00:15:55 - 00:17:10)
Continuity mistake: When Walt is sitting on the overpass it is clear that his car is parked on the part that straddles the median between the lanes, but when the shot is inside his car the view appears as if he is parked directly over the right lanes of traffic. (00:43:50)
Continuity mistake: When Walter drops the plate, it shatters into four pieces, with one piece sliding to the edge of the frame, where it stops without splitting further. The other three are in clear view and are in three intact parts. We cut away and back, and now the piece on the right is suddenly shattered into several smaller pieces. Also, the fourth piece that slid out of frame is still there when Walt wakes up, and he picks it up with the rest. The piece that Krazy-8 grabbed was too small to be one of the original four pieces the plate split into, and the piece closest to him didn't shatter further. In addition, when Walter reassembles the plate, the pieces don't match up with what they were in the basement. After the mysterious second shattering, there should be 8 total pieces of plate. If the piece Krazy-8 grabbed broke off from another part, that would mean 9 pieces. Yet Walt's reconstructed plate has only 6 parts plus the gap for Krazy-8's piece. Also, the final plate has smaller pieces at opposite ends, which wouldn't be possible given where the quadrants broke. Walter reassembles the plate upside down, so the part on top to the left of the gap (combined with the piece that is missing) is likely the piece that slid toward Krazy-8. So the large solid piece to the right of the gap would have been the piece that shattered into 5 pieces, but it is intact here. There is also a smaller piece between the piece Krazy-8 could have broken his piece from and the piece next to it, but this piece couldn't have come from either piece when the plate broke or if Krazy-8 broke his piece off the other piece. When Walter picked the pieces up, the piece closest to Krazy-8 was a single piece. (00:23:50 - 00:36:50)
Other mistake: Walter's pants flying in the air defy the laws of physics. The RV is racing forward and the pants somehow find themselves in front of the RV floating through the air. One could say that the pants perhaps flew forward when the RV 'hit a bump' perhaps. However the RV would have to hit a considerable sudden stop to get the pants to fly forward. The RV then runs over the pants which have fallen to the ground from in front of the RV. This could be ignored as somehow possible due to some strange anomaly. Except near the end of the episode. We see the same pants fly off the mirror of the RV flying backwards. Making it impossible for those same pants to be run over from in front of the RV especially due to the speed at which they are flying backwards straight into the camera shot. (00:00:15)