Tolerances on squares will not mean a lot to most of us, and are rarely relevant once you own the square, due to the way we handle it, store it or heaven forbid drop it. :shock:
When buying a square it is best to reverse it to check for 'square' as, if it is square it stands the best chance of staying square. 8)
I use my own apprenticeship made Squares both Standard Engineers and Centre Square, both now over 20 years old and still square.
In days of old, Engineers Squares would also be lightly tapped to return them to Square as this would move the pins holding the blade to the stock, this as others have said is bad practice as it does indeed loosen the joint and increase inaccuracy.
The only problem I would foresee with tapping a Japanese square would be the possibility of the square going out of flat(bending) which could render the divisions marked upon it inaccurate.
Ranting ramble over
Bean