Show Title: Kang and Kodos passing by in their flying saucer.
Billboard Gag: Moe's Tavern: We accept most fake ID's. (with Moe pictured holding an obvious fake id with Nelson Muntz's picture bearing the name John Q. Legal, Age: old enough.)
Chalkboard Gag: I will stop asking when Santa goes to the bathroom.
Couch Gag: Set at a used couch lot, the dealer activates an air pump that puts wind puppets with each of the Simpsons' likeness in motion as a means of advertising his business. When he departs, Bart's comes to life, takes a pair of scissors from the dealer's back pocket, and cuts Homer's loose, sending him flying into electric wires that proceed to shock him, leaving the Bart puppet laughing in amusement.
Final Cut Pro
The "Pro Movie" video-editing software Bart uses to compile footage of the President speaking that Bart should go on the submarine is a parody of Apple's Final Cut Pro video-editing software. It has been available since 1999, and has been very popular with many editors (and still is.) The Simpsons Movie was also edited on Final Cut Pro. The name of the software seems to be a combination of "Final Cut Pro" and "iMovie," the latter being Apple's consumer-level video editor.
The submarine jumping over the little boy's head in Skinner's submarine video is reminiscent of the ending of Free Willy, where the whale jumps over the little boy's head.