This is the second of five times the theme song was interrupted. The other times were: Whistle While Your Wife Works (2006),He's Bla-ack! (2014), A Lot Going on Upstairs (2016) Inside Family Guy (2016) V is for Mystery (2018).
During the USO show, Peter makes a joke about his golf skills and says "Just wanted to remind you fellas what you're all fighting for". These are variations on regular jokes made by Bob Hope in his USO shows during World War 2, the latter joke usually involving dancer Patty Thomas.
If Peter had 400,000 fake lottery tickets printed up then he was likely committing fraud which is a felony.
During the opening credits one of the showgirls states that Peter got her pregnant however it was established in Sibling Rivalry that Peter got a vasectomy though it is likely that he had it reversed.