GB1- The whole thing is so darn original, and makes such good use of time, that I'd almost entirely leave it alone. However, I would include a few short scenes of Egon and Ray building and/or testing the equipment (causing a few explosions and the like). I'd include a short story of how or why Winston went in for an interview, something funny. I'd also make a big distinction between ‘ghosts’ and those ectoplasmic monsters (including Slimer). I'd have the GB's wondering what these weird things were (leading them and audiance to believe they're not natural ghosts, but maybe demonic creatures for the coming of Gozer)(the fact that they're called Ghostbusters yet they're constantly fighting these things that are nothing like a classic ghost bugs me).
GBII- I'd include Winston in: the snippets of the GB's at their new jobs. I don't know exactly how you'd sedgeway his job in there or what'd it be (we know he's been a contractor at times), maybe some scenes of after the party Ray driving Winston to work in the Ecto-1, with some guys at work gawking and maybe laughing.
Atleast explain why Winston isn't digging the hole. Have Peter joke that he's not a scientist so he doesn't get to come along, or have Winston blatantly say he won't because he's afraid of what'd happen if/when they're caught. Have Winston for the court scene, fine don't give him a proton pack, let him work the traps then!
Exclude Janine and Louis's romance, for that matter a lot less of Louis. Sure let him want to be a GB, but just tag it on.
In a perfect world, Slimer would look the same as in GB1. I know the mold was stolen, I know…
Have Jansosh use a few more demonic powers. It was a little stretch from having lights for eyes (which I felt was a GREAT touch, probably the best effect and coolest thing a ghost/villain has done in the whole of the two movies) to being a ghost nanny. Have a place in between showing a few more powers (maybe replace Louis for Jansosh in that scene never done for GBI, where two thugs were to corner Louis, that'd fit even better here!).
Wow, I guess I do have a few ideas…