As the condition to having LeVar Burton appear on his final recording of "Fun With Flags", Sheldon agreed to erase LeVar's contact information while he watches. As he has mentioned on numerous occasions, Sheldon has an eidetic memory. He would remember the information anyway.
The bottle of champagne found in Roger Abbott's office is said to be 50 years old. Champagne cannot be kept that long, even very good vintage bottles can only be kept 10 to 15 years. After 50 years, this champagne will have lost its bubbles, so Sheldon would not have been able to pop the bottle.
During the highlights of "Fun with Flags", on the beach scene, at the bottom of the screen, there's a clearly visible visual distortion (looks like static) between the feet in the "sand" and the actual green screen rendering.