Revealing mistake: In the scene where Leonard is supposedly playing Halo 3 against somebody in Copenhagen, there is no ethernet cable or wireless adapter connected to the Xbox 360 (one of the originals without wireless inbuilt), which means that there is no way he can be playing online with someone in another country.
Continuity mistake: When Penny asks Sheldon "What trauma?" in the electronics store, Sheldon holds two boxes - one with an orange side on top of one with a black side. In the next shot the black sided box is on top of the orange one. The boxes then continue to swap places during the whole scene.