But now, I'd like to turn to a different area. What are some of the tenants and practices that are uniquely (or nearly so) Mormon that we'd view as positive?
They're into frugality, not wasting money, not gambling, not going into debt, etc. They have a weird sort of recommendation for food storage, saying that everyone should keep a year's supply of food and basic necessities on hand. They also recommend things like having a garden if possible and knowing how to do basic practical skills like home canning, cooking from scratch, sewing clothes, etc.
It's sort of like survivalism, but in my limited experience they don't tend to go over into the nutty fringe by fantasizing about an end-of-the-world scenario. It's not as much preparation for the apocalypse as for preparedness in case of losing your job, a natural disaster when the store shelves get empty, etc., though I'm sure there are a few on the fringe use it as an excuse to get all ready for the zombie apocalypse.
We don't literally do the food storage thing, but we have plenty of savings, and have just naturally picked up the basic skills. I was debt-free already when I met my wife, and I probably enjoy gardening and making stuff at home more than she does.
In a lot of ways, I'm probably as
culturally Mormon as she is, if not more so, and was that way even before we met, which is why our marriage works so well. On the other hand, when she wants an excuse not to follow cultural things, like the recommendation to have lots of kids, she gets to blame it on her atheist husband. Because wives are supposed to respect their husbands, she reluctantly has to go along with my choice not to make her give birth to a bunch of rug rats.

So it's a symbiotic relationship.
The church also has storehouses of stuff that they give to the needy, who aren't required to be members of the church:
http://en.wikipedia.org/wiki/Bishop's_storehouse
They're also into genealogy and preserving historical records. It's tied up with the whole concept of Baptism for the dead, but the side benefit for normal people is that a heck of a lot of historic information gets preserved, microfilmed or put online that wouldn't otherwise. Their website familysearch.org has some stuff I haven't found elsewhere online that was crucial to some research I was doing recently (early 19th century Louisiana estate records and Massachusetts death certificates, in that particular case).