What Could Have Been: Originally the plot was to have them visit, and therefore accidentally cause, all of history's greatest tragedies (the sinking of the Titanic, the crash of the Hindenburg, the Black Plague...).
The time machine was originally a pick up truck, then a van. It was changed into a phone booth because it might have made the movie too close to a Back to The Future ripoff. Now it's just an unintentional Shout-Out to the TARDIS in Doctor Who.
Eddie Van Halen said that he would have been glad to appear in the movie, but nobody asked him.