Matt Bomer was actually able to make the shots while skeet shooting due to having had experience using a gun as a kid for hunting with his dad.
Neal smacking the chess pieces off the board wasn't CGI - Matt Bomer really did it and one hit the camera. In the commentary he mentions he ended up with a large bruise on his hands due to the pieces being made out of a heavier metal.
The bar in which Neal meets Avery is actually a library dressed up as a bar.
In the commentary, Matt Bomer and Tim DeKay both talk about how Matt kept holding his breath (unintentionally) each take until he almost passed out for real.
While filming White Collar, Tim DeKay rented an apartment from Jonathan Tucker (Avery).