Read other letters about this article
I agree that "mistress" is problematic for all the reasons you suggested. I also think "girlfriend" is bad... she's a woman with kids and a career so anything "girl" irritates me. "Other woman" seems fine, but doesn't pass the "what about him" test. So if you were writing from the perspective of what she did, is he her "other man"? No... because "other woman" carries the connotation of possession. He has his wife and he has his other woman, both things he has collected.
But there wasn't much of an argument against "lover." It does pass the "what about him" test. It makes you uncomfortable? Well, maybe that's appropriate. To me, it's telling it like it is. Why search for a euphemism?