I have the original DVD set of Invisible Man and sequels (though I've yet to watch Invisible Agent, which is odd) and the movies all hold up pretty well, even the Abbott and Costello one. Sven is showing this tonight, so I'll tune in. Rains is so good in the movie and we only see his face once.
The movie is also quite funny, and intentionally so. It's also ever so British, which is something else I enjoyed as a kid, even if they said things that didn't always make sense to me.