When the first kid is in the White House basement you see "C. Clinton" most likely for Chelsea Clinton written on the wall however this movie presumably takes place in 1996 when Bill Clinton was still in his first term therefore would still be living there.
Final on screen appearance for Sonny Bono. Bono, who was serving in the U.S. House of Representatives at the time of the film's release, played himself as a Congressman coming to the White House to see the President.
In the opening scene at Tyson's Corner mall, Simms' tie changes from a brightly, multi-colored tie to a brown tie when confronted by his supervisor at the Dunkin' Donuts stand (which Simms refers to as an "ugly, brown tie") and then back to the multi-colored tie when he is being promoted to guard the First Kid in Morton's office.
Sam Simms: You know what's gonna happen if I let you go? Morton is gonna call me in. Then he's going to chew my butt off. I'll be sitting there and my butt's gonna get smaller and smaller and by the time I get up, my back is going to be on my thighs. Because I won't have no butt. You wouldn't want that to happen to me, would you? Of course you wouldn't.