I know I shouldn't have jumped down the hole to enter this dungeon but I did. Usually there is a back door or some way out when one does something stupid like this but I have completed what I had to do there and now I am stuck. I don't have any of those handy levitation spells that were easy to find in Morrowind and Oblivion. Is there another exit that I haven't found? Is there somewhere I can get one of those spells? HELP! Spoilers welcome.

If you follow the dungeon through to completion it'll take you back out of it. Go through the door behind the sarcophagi the boss emerged from. That'll take you to an end chest and up a tunnel that pops out through a hidden door into the chamber above the pitfall

Good Grief I didn't see any door - I knew there had to be one - thanks a ton!

How do you lower the bridge in Geirmund Hall?

There are two levers near the drawbridge. One visibly on the ground (trap) and one on the wall behind the Dragonborn when looking at the drawbridge, obscured by a root. The one on the wall drops the drawbridge.

http://elderscrolls.wikia.com/wiki/Geirmund

That one took me about half an hour to figure out, too. I had to give myself a slap for being so stupid, but it's easy to miss so dont feel bad! As the lady above said, the real switch is behind you when you face the dummy switch, it may be hidden behind some hanging moss