I'm one of those people who believes that pronunciation is vital. Accent is just one of those things that we really can't help sometimes, but getting the stress right on a word is very important.
I'm finding this more and more in Spanish, even with words that I think should be perfectly understandable no matter where I put the stress. For example, the word "difficult" is "difícil", with the stress on the second "i". However, I tend to pronounce it "dificíl", perhaps because that's how it is in French. A couple of times I have described something as "muy dificIl" with the stress in the wrong place and been met with blank looks all round. When I finally realise, and say it correctly, everyone understands!
As others have said, it's extremely important to get the stress and the pronunciation correct with words which might easily be confused with other words.