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 Transporter Malfunction - S5-E20
Continuity mistake: Sheldon opens his transporter box and takes out Mr. Spock, while making a big deal about it remaining mint in box, unopened. Later, he makes a big show of using an exacto knife to gently open the box with Spock in it.
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.