Recently, a colleague of mine pointed me to a MathSciNet review of one of my papers that is completely off the mark - it is not negative or anything like that, but it grossly misrepresents the contents of the paper (when describing the origins of the techniques and questions in the paper, for instance, as well as the "position" of the results within the current litterature and the meaning of the results themselves).
I'm not sure what I should do - actually, I probably won't do anything because the paper seems pretty inconsequential and the quality of the review most likely does not matter much. Still, the same thing could have happened with a paper I truly care about, and this led me to wondering what the proper behaviour is: should I contact the reviewer and ask him/her to retract his/her review (explaining why, of course)? Should I contact MathSciNet and let them know that I believe the review is incorrect? The first option raises some "diplomatic" problems, while the second one seems to me both to be abrupt and to waste several people's time... I think, if pressed to act, I would choose the first course of action, but I'd be grateful for any suggestions (e.g on how to say "you absolutely mangled that review!" without being rude..)
Final note: I'm asking this question anonymously because I don't have that many papers and it would be easy to identify the reviewer by looking at my MathSciNet profile, and I'm not out to embarass anyone.
Thanks for your help - if the question is inappropriate for this site then please close, of course!