I'm fine as long as the basics are present and the characters still have basically the same personalities. I don't really care if they're plunged into completely different situations that never happened in the comics, so long as it doesn't change the characters personality too wildly.
I think it's important to remember the source material to an extent - HOWEVER it's often said that The Watchmen was one of, if not the most faithful adaptation of source material - and it got absolutely panned by critics and probably only broke even at the box office (despite making lots of money for it's rating - it's production budget was just too high for what it made).
I guess the thing is - general audiences. They're not necessarily entertained by the same things as CB fans are (probably one of the reasons they're not CB fans). They don't have back-story or context. Remember they only have about 2 hours to tell a story that might involve years of various factors to a CB reader. I say leave the "faithful" adaptations to animated movies, and just let them "respect" the character for films as others have said. Even then they can take liberties in my eyes (to an extent) since a writer and director might have a different perception of the character than me as well.