I just watched this tonight, having only seen it once before as a kid.
As I remember, there was a scene that is not in the current version:
To prove he's from the future, Tom accurately predicts a solar eclipse.
Or is this from a different film entirely?
Bing Crosby predicts a solar eclipse while in the past to avoid being executed in a movie, but I don't remember what the movie is.
As for whether or not a seen like that is in "Oddball" it does seem like there was a scene with an eclipse, but I might be mixing it up with the Crosby movie or something else.