Sheldon and Barry Kripke decide to settle who gets the vacant office with a basketball contest because neither of them are any good at sports. However, in a previous episode Kripke is shown to be an experienced rock climber, and in a later episode Kripke is an amateur fencing instructor.
When Penny is adjusting the painting, the way she turns it is opposite to what Amy says.
When Sheldon complains about the shrimp, he says he can't decide "which order to eat them in". Sheldon would have said, "in which order to eat them".
Penny says to Bernadette that the portrait of her and Amy is "kinda heavy", meaning difficult to lift. But both she and Amy individually are able to pick up the painting without any significant difficulty.