As regards rotating the map, I don't when using a road atlas (bit too hard to do so when a large one), so have to do the mental rotation as regards 'take the 3rd left'. With OS maps and going across country, that would make more sense to rotate. especially where you need to try and align physical features of the landscape that you can see with their abstract representation on the map.
Jigsaws, I rotate the pieces, but there is also some mental rotation going on as well, when guessing which would be a piece worth bothering with. The missus (engineer so should be good at the mental rotation) is useless at pattern-matching for jigsaws (or perhaps just takes the engineers approach of if we take a bit off here, THEN it will fit! Why she isn't allowed scissors when we are doing jigsaws!)
I'm failing to find anything significant so far as regards mental reflection (mirrors!), and possible sex differences....................
Wondering about links between mental rotation ability and evolution.........if men did all the flint knapping and hunting (supposedly hones mental rotation skills), whilst the graceful laydees did all the gathering, then surely the gatherers should be ace at map reading (since they need to orient themselves in a landscape and be able to find good food sources again -- you can't just potter about at random and assume you'll stumble across a tuber!). Although AFAIK, we don't even have evidence that the muscley males did the flint knapping in the first place. And I bet something ladylike like basket weaving requires similar mental rotation skills to flint knapping anyway..............