Good question!
I'm running The Shackled City. The player's characters have been converted to Pathfinder RPG rules, but I'm running the campaign and the monsters as is.
For me, no conversion is really necessary other than converting a skill check or something similar, here and there. However, it would be possible to do lots of conversion if I were to truly convert all the statistics of the various monsters to 100% Pathfinder. But, I only do that when I have time and if I really think it's necessary.
This thread might help, too:
I ran Legacy of Fire for Pathfinder. It needed very little tinkering.
The subsystems don't translate well. You can find folks who have translated most of it and let you use their version.
For the most part I just run them. If a monster comes up that has a Pathfinder equivalent then I use it, else I use the old 3.5 stats and calculate CMB/CMD as needed.
I've run a good amount of old Dungeon Adventures and 3.5 modules on the fly this way and it works for me.
I ran Savage Tides with Pathfinder PCs and the biggest problem that came up was that there were two paladins in the party. That AP gets really demon heavy so that skewed things in the PCs favor. Next time only one paladin.
Hardly any. Since the monsters are usually around for just one encounter, their stats don't matter as much as the PCs. Heck, I've even run D&D basic modules from 70s and 80s with little change. Occasionally, I just had to substitute stats from the Bestiaries for the ones listed in the modules.