What does a bad tweeter sound like?

If you have a capacitor short in the tweeter path, you may get a lot more mid/bass (a dangerous thing!)

If it is louder than normal, check your crossover. My experience has been either a crackling distortion or at certain notes you get a break up in the sound.

Whenever I "question" a drivers performance or simply want to conduct my own "test", I find that a 20 - 20Khz audio sweep is useful.
https://www.youtube.com/watch?v=PAsMlDptjx8

Thanks all....I just removed the tweeter from my Vandersteen 5A (left side) and am sending it back to Vandersteen for a rebuild.  I hear just as you describe...louder on that speaker, fuzzy and metallic on some frequencies.   I thought it was the midrange, speaker, but removed that one last month, got it back rebuilt, and the noise is still there.  I hope its the tweeter.