Here is an article (with embedded TEDx talk) on more thorough research being done at the Dance Psychology Lab at the University of Hertfordshire.
The most interesting conclusion to me is that choreographed dance raises your level of convergent thinking (questions with one answer, like math problems), while improv dance raises your level of divergent thinking (open ended questions such as "What are some alternative uses for this brick?").
I recommend viewing the TEDx talk embedded in the article, which goes into more detail on that particular point, I believe.
Aside from all the boring stuff about fertility, hormonal background and dance attractiveness, there's a fascinating bit at the beginning-- Peter Lovatt, the presenter, was close to illiterate. However, he was a very good dancer, and by the time he was 22, he figured out how to apply the sort of memory he needed for dancing to be able to focus on reading. Later, he got a masters in mathematical modelling of brain functioning.
I wonder how much can be accomplished by encouraging people to build on their strengths rather than trying to remedy deficits by using the same methods people who don't have those deficits use for learning.
Frequent dancing causes a 76% reduction in the risk of dementia. The benefit seems to be from freestyle social dancing, though I don't think that part is as well-verified. The benefit seems to be from making large numbers of quick decisions.
I wonder if playing jazz has similar good effects.
For something a little geekier, Shiva Nata, a system of keeping the mind fresh by doing more and more complex movements. The author of the blog is a silly person, but the system seems to be for real.
Edited to correct html which was entered in the text field instead of the html field. It wouldn't surprise me if having to deal with electronics and computers tends to prevent dementia, considering the number of fiddly and changing details one has to deal with. Or is fun required?