I actually worked on an update myself a year ago and fixed some bugs, but never finished it completely. If you like, I can send you that as a starting point.
The only reason PI doesn't use all the new models automatically is that it needs larger turret FOVs for some of them, so it included modified versions of the original models with those changes (the HTL versions didn't exist back then). I think one or two models had different mass or MOI values as well. The best solution to this would be a way to override any model FOVs in ships.tbl, but a feature like that has to be added to the game. There is also an alternate version of the final mission with slightly different camera positions for the HTL models, which I already updated for the HTL Hatshepsut.
It would be great if the Saturn model could be upgraded as well, based on the new Hades, but that may take some effort with the turrets and retexturing. I think the last mission would need to be retested for balance as well.
The last time I played PI, I was also seeing slightly different AI behavior in some missions, although I don't think there were any major differences with the mission balance. I recall this was an issue in missions 9, 10 and 14c, which may be worth playing in the old 3.6.7 build and comparing with a current one. 14c had a more severe AI issue that sometimes broke the mission. I did something to fix it last year but can't remember exactly what now.
There is also a generic bug in FSO where the briefing icons are positioned for the 640x480 interface, regardless of the resolution. This is not specific to PI but makes the mission dates/times look kind of strange. I reported it on Mantis some years ago but it's still in the game as of 3.7.2.