Believe it or not, there weren't a lot of "made-up" characters, just versions of old characters that were completely unrecognizable. Callisto, for instance. My favorite part in X3 was when Kitty phased the Juggernaut into the floor and he busted out. What her power does is allow things to pass through each other, so he wouldn't have been 'stuck' so much as his legs suddenly shared space with the concrete etc. that was there.
Personally, I thought the dialogue was miserable throughout- which doesn't make any sense at all. Uncanny has always been a well-written book, but even "Ultimate" (the newer rewrite of the X-verse) contrasts sharply with X3:
Ultimate
Scott: ...And Nightcrawler and Marvel Girl are staying here in Harlem for
the uptown detail.
Jean: Are we seriously still going with "Marvel Girl"? I outgrew that
handle two bra sizes ago.
Kurt: At least you are not named after a worm, fraulein.
X3:
Prof. Charles Xavier: Something woke her. But she has to be controlled.
Logan: You know, sometimes when you cage the beast, the beast gets angry.
Generally, the movie focused on Wolverine the most (as did the first two), but it failed to really flesh him out as a character at all. The other two movies had already established his romantic sub-plot with Jean, and the way it was handled in X3 lacked depth (from my perspective). I also found that the Rogue, Kitty/Bobby, and Angel subplots all had a ton of potential and very little payoff.