Goof: Captain Holt says "I did some research on amicable breakups. I visited www dot ladiesgoodhealthmag dot com backslash sex hyphen relationships backslash 8 6 7 5 9 9 9 0 4 backslash 9 4 3 2 ampersand 2 0 dot html. Do you know that site?". Websites use slashes, not backslashes.
Goof: When Gina notices that Jake is finally at the wedding, she calls him "Andy" (the actor who plays Jake is named Andy Samberg).
The game that was on when they busted the illegal gambling was the Ole Miss at South Carolina game played on September 24, 2009. In the show, South Carolina was ahead 16-3, and they ended up winning 16-10.
The cast actually went though police and firearms training, which is unusual for a comedy series.