Is it considered rude to point out typos, by sending an email to the reviewer, in a MathSciNet review? Is it considered rude to point out typos, by sending an email to the reviewer, in a MathSciNet review?

Will they be able to correct the typo, easily, with out involving MathSciNet technical team?
It is better to send the corrections directly to MathSciNet, through the mathrev "at" ams.org account. As long as they are just typos, we update the review directly. If you notice mathematical mistakes, we tend to involve the reviewer (if possible), since the changes will be more significant in that case. 

We routinely update files for which we discover problems of this kind. It is not a problem. We appreciate your help in this regard!

As for the question of rudeness: I don't think it is rude, these things happen, and if you phrase the matter politely, it will probably be appreciated. On the other hand, reviewers cannot update directly published reviews, which is why it makes more sense to contact us instead.