In the last scene Howard pulls out a deck of cards to play the "magic" trick on Sheldon again. When Howard pulls out the deck of cards you can briefly see the very bottom card is a two of hearts. However, when Sheldon picks out a random card from the middle of the deck, it turns out to be the two of hearts. Not only is this a continuity mistake, but it also implies that they had a deck full of two of hearts cards.
When Priya talks to Leonard about getting contacts, the way she holds his glasses changes between shots.
It doesn't make sense for Leonard's vision to be worse with contact lenses. They may be uncomfortable but that wouldn't make his vision blurry. Even if they did, he wouldn't have been able to drive to work.
When Leonard gets his contact lenses, he should not be knocking everyone over in the University Canteen, as when the camera pans to show what Leonard sees, it shows that he can see where people are, just can't see who they are. And no Optometrist would ever let someone go, without checking their vision. With Leonard supposedly being a genius he would know that.
Uranium-235 is nuclear weapons grade fissile material under the strictest international control but only a fairly weak emitter of radiation (as long as you don't pile too much of it together and cause a criticality accident), which makes it an illogical choice for Sheldon as a radiation tracer.
When demonstrating his magic trick to Howard, Sheldon has him pick a card from the deck, and then scans the bar code on the card with this "magic wand." It's already been established that Sheldon has an eidetic memory, so memorizing the 52 bar codes on the cards should be no problem for him, eliminating the need for the wand and the transmission to his cell phone.