When Penny is talking to the guys after the shift, she suddenly has a yellow paper in her right hand without picking it up anywhere. The paper then disappears again when she is standing at the door and says her last line.
When Penny enters Leonard and Sheldon's apartment after her work shift, Leonard is in his socks. After Penny exits the apartment he's in his shoes again without even taking them in hand.
After Leonard throws the Caution tape on the floor, it disappears between shots, then reappears rumpled up differently.
When Leonard is dusting off one of his collectibles a yellow Post-it note can be seen on the back. In the next shot it is missing.
Sheldon states that Captain Kirk will steal a cloaking device from the Romulans in 2328. Kirk's era was set in the 23rd century, which would mean the correct year would have been more like 2228. In any case, The Original Series has been retconned to take place exactly 300 years on from the original production, so that an episode first shown in 1968 is now canon to have taken place in 2268 - something Sheldon would be aware of.
Throughout the episode the main control lever of the Time Machine is pulled toward the passenger to start it and pushed away from the passenger to stop it, but this is the opposite of how it functions in the original 1960 film.
Sheldon states that in The Time Machine (1960) the human race has split into two "factions". It had actually split into two species.
When bartering for Leonard's share of the time machine Raj offers his "original 1979 Mattel Millennium Falcon with real light speed sound effect". However, Mattel didn't make Star Wars toys, they were produced by Kenner.
Sheldon refers to Hello Kitty as a feline.
Hello Kitty is not a cat. She is a little girl.