I can't say I have anything big to add about the bureaucratic stuff after paying off the mortgage. I paid mine off in 1998 after first taking it out in 1989 and refinancing it in 1992 at nearly 5 points less.
It was for a co-op apartment so the bank held the apartment's original stock certificate, not a deed. I had been paying off large chunks of the principal in 1997 and early 1998 so the final payoff amount was not for a whole lot. I arranged for it to be made via electronic payment the same way I had been making my regular payments, saving me the trouble of getting a bank check. The mortgage company was very co-operative with me and enabled the process to go very smoothly.
A few weeks later, I received the original stock certificate along with some other relevant documents. I did not have to do anything with regard to filing documents with the county clerk office although I don't know if the bank did.
I can tell you that it was great to lose that monthly payment, one which had been growing the previous few years as interest rates rose (it was a 1-year ARM). I was still working full-time, so now one biweekly paycheck was enough to cover all my monthly expenses most of the time. This enabled me to quickly replace money in the mutual funds I used to pay off the mortgage.
One small downside of doing this payoff was that I had to adjust my W-4 withholding exemptions downward because of the loss of the home mortgage interest deduction (most of it, I still had my co-op's interest). This was equivalent of giving myself a small pay cut.
Greatly lowering my monthly expenses was a key step towards my ER, as I was easily able to afford to switch to working part-time a few years later, along with its 40% pay cut. Once I saw how well that was working out, I was able to fully retire in 2008 at age 45.