The Vacation Solution - S5-E16
Character mistake: In Amy's lab, when she is complaining to Sheldon how she gave him the simplest tasks, and that they're still not done, Sheldon replies with how Einstein failed math because he wasn't challenged, and that it is the same case with him. Einstein never failed math. Sheldon of all characters should know that.
The Rothman Disintegration - S5-E17
Continuity mistake: After Amy returns to the apartment for the Grease DVD and discovers Penny doesn't like the painting, she then exits the apartment with the painting and the DVD with her. When Amy says to Penny she doesn't need her pity, the DVD is placed above the hanging string of the painting. In the next shot, as she walks into the hallway, the DVD is suddenly almost half below the string.
The Werewolf Transformation - S5-E18
Continuity mistake: When Penny is giving Sheldon his haircut, she accidentally shaves the back of his head. The clippers are going from the bottom of Sheldon's hair, up to the top of his head. When Sheldon goes to leave the room, it can be seen only four or five inches from the back of his head have been shaved off.
The Werewolf Transformation - S5-E18
Character mistake: In S5-15, Sheldon is asking his friends to take him to SuperCuts. But in this episode, he goes to Mr. D'Onofrio's barber shop where he says he's gone to since he moved to CA, and he said D'Onofrio had his "haircut records."
The Hawking Excitation - S5-E21
Character mistake: The sign on Howard's laboratory door reads "RESTICTED area".
The Hawking Excitation - S5-E21
Continuity mistake: When Sheldon is trying to convince Howard to let him meet Stephen Hawking, Howard places a water bottle on the table he is sitting in front of. In the next shot, it appears in his hand again.
The Hawking Excitation - S5-E21
Continuity mistake: When Howard and Bernadette are in his bedroom, there is a bottle of Vitamin Water to Howard's left. In one of the shots, the bottle has completely vanished out of frame, but returns in the next shot.
The Hawking Excitation - S5-E21
Continuity mistake: Penny is talking to Sheldon in the laundry room and places a box of detergent on the machine. The side of the box is facing her. In the next shot, the box has turned to face her.
The Launch Acceleration - S5-E23
Continuity mistake: In the scene where Sheldon is scooping spaghetti onto his plate, he pauses with the spoon in the serving dish. Shot cuts to Amy and the spoon is still in the serving dish. When shot cuts back to Sheldon the spoon is being held over his plate. Shot cuts back to Amy and the spoon is back in the dish.
The Launch Acceleration - S5-E23
Factual error: In all the episodes leading up to Howard and Bernadette's wedding, Howard was going into space to install a space toilet. But in this episode, Howard tells her they want his telescope, so he has to go.
Suggested correction: The space toilet was something Howard designed that NASA installed back in season 2. His mission to the ISS in season 5 was always about his telescope. In episode 5, "The Russian Rocket Reaction", Howard says NASA picked his team's design for the deep field space telescope that's going on the International Space Station in the spring.
The Countdown Reflection - S5-E24
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.
The Countdown Reflection - S5-E24
Continuity mistake: After Howard and Bernadette are pronounced husband and wife, when they kiss the camera angle switches to an overhead shot, but as it zooms out (to a digital image) things change - such as the configuration of the rooftop, or things move - such as the cable dishes, or things even vanish - such as air-conditioning units.
The Countdown Reflection - S5-E24
Continuity mistake: Penny mentions that she knows lots of people who got married in Las Vegas. In episode 7/9, she discovers that her "fake" wedding to Zach in Vegas was real.
The Countdown Reflection - S5-E24
Continuity mistake: Near the beginning of the episode, Howard said the launch was on the Friday before his planned wedding. They decide to marry before he launches, and they say they only have two days. Then he tells the clerk at City Hall that he launches on that Sunday. Too many inconsistencies.
The Countdown Reflection - S5-E24
Other mistake: Raj doesn't get over his selective mutism until the end of season 6. However, he very prominently speaks during Howard and Bernadette's wedding without alcohol or meds. In the season 6 episode where he finally does speak without any assistance, Penny makes a big deal about it so it's shocking when he does it here with no big shocks.
The Higgs Boson Observation - S6-E3
Continuity mistake: At the end, when Alex and Sheldon are at the apartment, when Alex says "she seems nice", there are two beer bottles on the coffee table. The camera goes to Sheldon, and when it returns to Alex, there is only one bottle.
The Higgs Boson Observation - S6-E3
Factual error: Sheldon tells Alex that he's run a background check, including her medical records. There is no way he could obtain medical records without a HIPAA authorization signed by Alex herself. It's illegal.
The Higgs Boson Observation - S6-E3
Other mistake: Just before Amy video chats Sheldon there is a shot where she is wearing glasses, and when the camera zooms out she isn't.
The Higgs Boson Observation - S6-E3
Continuity mistake: Sheldon is taking composition books out of a box that was sent to him. When he first starts pulling them out, he has two composition book in one hand. Two shots later, he has only one composition book in his hand, but he is picking up a second one.
The Extract Obliteration - S6-E6
Continuity mistake: Sheldon is sitting by himself at a lunch table with an opened bottle of water with the bottle cap in front of the bottle. Raj and Howard arrive, and in one of the shots, the bottle cap moves closer to the bottle by itself.