Actors have to have good diction.  I don’t care what sort of character you are playing or what their accent is.  Diction is essential to comprehension.  Remember, the audience has never heard these words before, or at least, you should assume they haven’t.  (Even if you’re doing Shakespeare, operate on the assumption that at least some of the audience has never heard or read Hamlet before.)

Diction relies upon consonants being fully pronounced.  American English is much more focused on vowel sounds than consonants.  British English is the reverse.  The British use their lips much more than Americans do (if you’re doing a British accent in a play, and doing it well, you’ll find that your lips will get fatigued in your first week or two!), and this contributes to the fact that their diction is so much more precise than ours.

I’m not suggesting that you use a British accent, but you should be sensitive to the fact that we Americans sometimes get very lazy in our speech and so glide through the harder consonants that help to define the perimeters of words.  In real life, I can ask you to repeat something if you’ve slurred a word.  The audience can’t do that.  So you need to be sure that you are more careful in your speech when you are onstage than you are in everyday life.