The Creepy Candy Coating Corollary - S3-E5
Continuity mistake: At the dinner, Howard's mom calls. Howard's wine glass refills itself between shots. (00:15:20)
The Staircase Implementation - S3-E22
Character mistake: In 1-14 "The Nerdvana Annihilation", when Howard says they should put the time machine into the elevator, Leonard states the elevator had been broken for two years. But in this episode, we found out the elevator broke seven years earlier. (00:03:10)
The Luminous Fish Effect - S1-E4
Continuity mistake: When Penny comes into the apartment to ask if Sheldon needs anything from the market, between the few shots, the position of the napkin and the pile of eggs on the plate he is holding changes. (00:05:15)
Factual error: Every time we see Leonard's laser lab the door is open and he is able, if the story requires it, to fire the laser. As evidenced by the several safety notices visible and the scripted requirements for characters to put on safety goggles it should not be possible to activate the laser while the lab door is open - it would be interlocked, meaning the laser wouldn't function unless the door is closed.
The Beta Test Initiation - S5-E14
Character mistake: Sheldon says (during Fun With Flags) "But like the flag over Fort Sumter, I'm still here." The Sumter flag was lowered when the fort surrendered to the Confederates. The flag over Fort McHenry was never taken down despite the British bombardment and inspired Francis Scott Key to write the National Anthem about it. Whouldn't a vexologist know that?
Suggested correction: Sheldon is referring to the actual Fort Sumter flag, which still exists and is on display at the Fort Sumter museum.
Sheldon is not referring the actual flag (especially since if the actual flag is in a museum it's not still over Fort Sumter). Sheldon is referencing the line from The Star-Spangled Banner "our flag was still there." Key wrote The Star-Spangled Banner after seeing the flag over Fort McHenry was still there. The writers simply made a mistake and Sheldon the character would know which flag inspired the line. Incidentally, the actual Fort McHenry flag also still exists.
The Large Hadron Collision - S3-E15
Continuity mistake: Penny asks Sheldon if the roommate agreement contains something about girlfriends, which Sheldon dismisses as unrealistic. However, it was revealed in season 2 that there is a cohabitation rider. This was revealed when Sheldon asserted that Leonard's girlfriend, Stephanie, was officially living with them.
The Herb Garden Germination - S4-E20
Other mistake: When Sheldon and Leonard are playing Archery on Wii Sports Resort, Sheldon presses the Z button on the nunchuck controller to fire the arrow, which is incorrect. When Leonard plays, he holds the Z button as he prepares to fire, then releases the Z button to fire, which is the correct controls. (00:03:00)
The Robotic Manipulation - S4-E1
Continuity mistake: In the ER, the glasses around the nurse's neck move instantly without her touching them. They go from angled to straight instantly. (00:17:45)
The Fuzzy Boots Corollary - S1-E3
Continuity mistake: When Sheldon, Howard and Raj play Jenga, there is one block sitting at the top of the tower. When Leonard walks in, there are now two blocks at the top, before we actually see Howard place the second one on the top. (00:08:10)
Continuity mistake: When Penny is squirting chocolate syrup in the ice cream container, she drizzles some on the lip of the carton, causing it to run down the outside. The camera switches to Leonard and then back to Penny, at which point, the chocolate is gone. (00:04:50)
The Zarnecki Incursion - S4-E19
Plot hole: While it would certainly destroy the entire plot of the episode, Sheldon could have simply contacted Blizzard's customer support to get all his stuff back.
The Contractual Obligation Implementation - S6-E18
Factual error: At the end of the episode, the girls are at Disneyland in costume as Disney Princesses. Adults at Disneyland are not permitted to wear character costumes because of the risk of them masquerading as Cast Members, so they certainly would not have been dressed that way at Bibbidy Bobbidy Boutique.
The Wildebeest Implementation - S4-E22
Continuity mistake: When Howard, Bernadette, Leonard and Priya are playing Jenga on the coffee table, the silver coffee pot, between the game and a coffee cup, disappears and reappears between shots.
The Irish Pub Formulation - S4-E6
Continuity mistake: As Raj, Howard and Sheldon are sitting at the table discussing leaving Priya alone while Leonard and Priya are away from the table, a water bottle sitting in front of Raj moves back and forth between his tray and Leonard's tray.
The Luminous Fish Effect - S1-E4
Continuity mistake: When Leonard and Sheldon are walking downstairs, Sheldon stops and pins back up the caution tape that is in front of the elevator. Between shots, the other strip of caution tape untwists itself. (00:01:25)
Audio problem: When Sheldon is knocking on Leonard's door at the start, the sound is out of sync with the action.
The Gothowitz Deviation - S3-E3
Character mistake: Sheldon refers to using the spray bottle as negative reinforcement when it is in fact positive punishment. Reinforcement involves encouraging a behaviour by either adding or removing a stimulus whereas punishment involves discouraging a behaviour by adding or removing a stimulus. Sheldon would know the difference.
The Adhesive Duck Deficiency - S3-E8
Character mistake: When Sheldon is placing his order near the beginning of the episode, he states "In the mid-18th century, King Rama IV of Siam..." King Rama IV was born 18th October 1804 and died 1st October 1868. His reign was during the mid-19th century (1851-1868).