Here are some things I could think of, some mentioned by others, other not.
- Wing spar location. Designing a cabin that will seat pax comfortably is hard as it is w/o having a wing spar through the top of the cabin. Much better to bury the spar in the cargo bay/fuel tanks... or better yet, have a wing box under the floor. Placing the wing spar in a hump above the fuselage as in some designs of course has a significant aerodynamical penalty.
- Wing load carrying structure. For a high wing, the wing part of the fuselage becomes a load carrying member of the structure and has to be made heavier. You have the fuselage and cargo hanging under the wing rather than standing on it.
- Gear design. With a high wing, you're stuck between a rock and a hard place. Body gear, which will be relatively narrow with the associated drawbacks. Furthermore, you will once again end up with the fuselage a load carrying member of the structure as it will have to transmit the gear loads to the wings, heavy with fuel and engines.
Your other option is to have a tall wingmounted gear (F50). Heavy, takes up lots of space, draggy when extended etc etc.
- Crash safety. If you have a high wing, you better make sure that it will not come smashing down through the cabin in a crash. Also, in case of ditching, it's much preferable to float on a low wing. Fuselages make very poor submarines!
- Emergency exits. The choice between high/low wing has all kinds of impacts on how you are allowed to design your emergency exits. I can't remember the pros and cons off the top of my head right now - it's been a while since I looked at that - but they were numerous.
- A high wing will enable you to put prop engines below the wing, giving you a larger effective wing area. Things hanging below the wing will not impact lift anywhere near as much as things sticking out of the top, as a previous poster suggested. Engine pods for jets are also beneficial. Fuselage mounted engines again place loads away from the wings where the lift is created, making the fuselage carry loads. Comet style engines probably won't happen again. Fire endurance, inlet/exhaust duct length related problems, the simple geometrical impossibility of fitting a modern high BPR engine in a wing...
- Etc. Etc. And Etc.
Compromises, compromises!
Cheers,
/ft