The chalkboard gag is a reference to The Adventures of Tintin, which was released (in the United States) only a month before the episode aired.
The music played in the background while people are watching Bart's clip is the same music as in the 1989 film Henry V during the St. Crispin's Day speech - both scenes deal with a rousing speech. This was also done similarly in "Boy Meets Curl" when Homer gives a speech.
Homer calls James Madison, Oscar Madison, a character from The Odd Couple.
When Homer's video is "Philippine prisonered," this is a reference to the Dancing Inmates of the Cebu Provincial Detention and Rehabilitation Center in the Philippines. The Dancing Inmates became YouTube sensations thanks to their interpretations of several Michael Jackson songs, including "Thriller" and "They Don't Care About Us."
The plane appears to be a Boeing 737-200 (note the cigar shaped engines that the 200 series have) which is an older model built from the late 1960s to the 1980s. Most major airlines have retired this model.
Bart says he's uploading the video to YouTube, but Milhouse is seen watching it on MyTube. It's possible that someone may have reuploaded it to MyTube.