Well Mark, as an installer and home owner I understand your interest. The only thing I don't do in my home is Drain Cleaning. I hate it. Luckily I have learned all the other trades to perform everything else I need. Here is what I would really worry about more than anything.
A1+ Pre measure all the new windows to make sure they will fit right.
1) - The drop cloths on the floor is important
2) - How they remove the old stuff isn't a big deal unless your hear a muffled cuss word or one guy running over to another.
3) - The installers should look for any visible water damage after removal
4) - Dry fitting is not needed. Make sure you have a gap around new unit
5) - Make sure the window is shimmed level from the under side
6) - If installing DH units, make sure there is a shim in the center on each side where the units lock together when closed. This keeps your vertical reveal straight. Your sash seal should be snug to the frame with no gap.
7) - Inside of unit should be tight to your inside stops. No gaps unless stops are not aligned correctly. Insulation should be around all four side of the unit.
- Exterior wrapping should be nice and straight. No gaps or sharp edges. Wrap should be caulked to the window unit and sealed around the outside.The caulk shouldn't be smeared all over your window.
9) - Area should be cleaned of all debris when done.
10) - Refrain from asking any questions about installation until job is completed. A lot of things are done in certain order by installers. Caulking is usually last thing done on all windows. This way we keep it off our fingers while working.
11) - installer should do a walk through and show you how to operate and care for your new windows when finished.
Hope This Helps!