Penny mentioned that her father's name is Bob but in the future episodes. Her father's name is Wyatt.
When Leonard serves his mother tea, the handle on the tea cup changes positions. Beverly grabs the handle with her left hand, but in the next second she is holding the handle with her right hand as she brings the cup to her mouth. The handle switches from left to right multiple times for the remainder of the scene.
When Penny and Beverly talk on their way to Leonard's apartment, Beverly asks Penny for details about her childhood and lowers her head. In the next shot, Beverly's head is at the height it was before.
As Leonard and Penny are doing tequila shots, the lime moves from Penny's hand to her mouth, without her making a move.
When Leonard is talking with his mother on the phone and Sheldon and Penny are trying to guess who he's talking to, Sheldon says that ears don't cross hemispheres. This is incorrect. Signals from both ears go to both sides of the brain.
Penny mentions that her father stopped calling her 'Slugger' when she got her first training bra, after which point she "wasn't slugger anymore", however in The Bachelor Party Corrosion (2015) while on the phone with him he calls her 'Slugger' repeatedly so he has apparently reversed his position on this matter.