Hmm.....what weaknesses you speak of? The only one is kyrptonite which doesen't exist on Earth and can't be manufactured synthetically.
Superman has been defeated and killed, but it happened at the hands of a being even more formidable than himself.
Yep, I remember it. It was back in 1992. I was a little kid back then. It was a being called "Doomsday" or some shit like that. It was like a Borg version of Superman, which had almost infinite strength and recovery ability and would adapt to anything you used against it.
SUCKMYMUSCLE
From what I've read in the IMDB boards, Superman gives Batman some Kryptonite "just in case", not to mention he has more weaknesses, like a Red sun (which, of course, Batman has no way of controlling) and mind control. If you read the thread that I linked to, the hardcore fans who've been following the comics for a while discuss the topic in-depth, with some interesting points.
There are guys here who are into it big time, like Man of Steel and mesmorph78, who should chime in.
BTW, the Doomsday saga was actually made into a feature length animation movie and was released in 2007. From what I understand, it's not faithful to the comic, but I saw it first without reading the comic and thought it was nicely done. Check it out if you get the chance. It's called Superman: Doomsday
http://www.imdb.com/title/tt0934706/