1. You can climb from a fall. You kind of know this because you'll catch yourself if you mess up while scaling a wall. But there's more to that: jump off a ledge into a wall and you can start climbing up it without plummeting to the bottom. Yes, you'll take some fall damage when you first start climbing, but it's better than splatting on the floor! Let's say you find a shaft from the south where you want to get to the path above on the opposite North wall; you can leap into the shaft and start climbing the wall without falling all the way down. Just make sure you hit the wall perpendicular because you cannot steer yourself while falling!
2. You can look around while climbing. Most people are probably too afraid they will mess up and fall to try this, but you can look around while you climb--helpful to determine how far up you are or if you've passed that ledge yet--however if you mis a step while climbing, you'll start moving in the direction you are facing, so you may fall all the way down! Also if you look all the way left or right you'll stop climbing and fall in that direction.
3. You can sidestep out of a climb. if you sidestep while climbing, you will start falling in that direction as if you just walked off a ledge. This means that you can climb up the north wall of a shaft and then sidestep to fall into an opening in the east or west side. This is a very useful trick in Woodbourne Hall--don't bother trying to solve his tricked out staircase, just climb up the wall next to the upstairs door and sidestep onto the platform. Ta-da!
4. You can climb backwards or sideways. You don't even have to be facing the wall to climb it! So long as your movement is perpendicular to the wall, you'll start climbing it. So you can back into a wall and climb up it so you are facing the room. The benefit to facing the wall, though is that it is MUCH easier to keep your movement perpendicular because you can watch the alignment of the wall textures to keep straight--much harder to do this from behind and even more so when sidestepping!
5. You can leap away from the wall. Climbing up a wall, start moving in the opposite direction. You just leaped away from the wall--well, more like as if you ran off an invisible ledge. If you are high enough above the ledge you want to land on, you just might make it (and sprinting helps). The easiest way to do this is to climb facing the wall, and then look a little to the left and then sidestep to the left; the end result is you moving directly away from the wall and falling in the direction of the new movement. Another safe way to do this is to climb backwards so you can see where you are and then run forward away from the wall when you are high enough.
Want to practice? In Daggerfall Kingdom, search for Tower Buckinging (seriously spelled like that). If you don't have it discovered yet, use the map cheat (CTRL+F1) or travel to the Lynx and Priest Inn and run 2 map pixels due East. The dungeon opens right up into the "sunken tower" block which is a huge open room with plenty of climbing opportunity.