In the close up shot of Leonard attempting to propose to Penny in the restaurant ("Two can play at this game . . ."), Penny's left arm is resting on the table when she say's "Get up." In the wide shot, that they cut to immediately, Penny's left arm is hanging straight down by her side.
Sheldon presents Amy with a document listing her as his emergency contact. Its title is "Sheldon Cooper, Caltech University employee information". The formal name of Caltech is the California Institute of Technology. The word "University" isn't in its name.
When Howard is describing his microscopic Valentine's Day gift for Bernadette to Leonard, there is a warning sign on the laboratory door with typo "resticted area" when it should read "restricted area". This is likely an inside joke. People are very quick to find fault, and it's not like the production team don't know. It's likely a joke.
The setting was Valentine's Day, yet in the restaurant there appears to be a Christmas tree behind Penny at one point.
Amy is wearing nitrile gloves while dissecting a brain, but she answers her phone while still wearing the gloves. She then doffs the gloves, and pockets her phone. She should have taken the gloves off before touching such a personal item.