>>Is it always wise for a retired person to pay off one's mortgage?<<


If you've owned your house for several years you've already paid most of the interest that's deductible. So, you have NO write-off(or very little) left.
In this case, you could pay off the house- and if you're post retirement income is still so large that taxes are eating you alive, you could buy a couple of duplexes. The rent would pay the mortgage, and you get the write-off. I hope this helps.
Eddie