I've done some research on pathfinding with the new climbing system because of a large number of military deaths I've started getting from elevated firing positions (among others). This is what I've found.
Normally your citizens and military will never climb or jump and will in fact report a job as incompleteable rather than use a climbable path to it.
I'm sure this is intended behavior. The reason for this is that there's an initial pathfinding process that only accept classical routes (i.e. walkable routes that do not go past locked or forbidden doors). If this pathfinding succeeds then the creature gets its goal set and a path is stored for it to follow. If it doesn't then the job gets cancelled.
The creature getting a set goal engages a second kind of pathfinding
So you know how creatures getting blocked from going a route they want to go can get that question mark on their heads and then they select a different route to their destination? Or when they're in a crowded hallway they start performing a shuffle past each other? They're doing alternate pathfinding. This part of the game's programming basically makes the assumption that if the creature got a set goal, the goal is in a sensible (generally walkable) location. Sometimes this isn't true. The strangeness is that this alternate pathfinding *does* make use a creature's ability to climb and jump and will path them over walls and in tree branches and stuff.
Combat overrides job pathfinding
Military units sometimes receive a goal that guides them to the nearest enemy unit. This often happens to missile units that run out of ammunition. What then happens is that the unit, instead of standing still because it can't path to the enemy unit, gets alternate pathfinding to the enemy unit which generally means climbing and jumping out of their cover to them. Unfortunately there are sometimes falls involved leaving your soldiers in the middle of an enemy squad, outside your walls, and stunned from the fall (and therefore defenseless). This typically kills the military unit. The same thing also causes babies without mothers to carry them to goal outside your fortress walls which typically means they climb over your walls and up chimneys to get snatched.
The same applies to enemy units. I always play surface fortresses because of the challenge (that's why I'm experiencing all these fall deaths, my archers are in arrow towers etc.). And enemies usually stay nice and docile outside even a 1 z height wall. But if the leader of the squad just happens to get a 'goal' inside your fortress then they will climb up and down branches over your walls and all their squadmates will also alternate pathfind to get to their leader, bringing the whole squad over your walls.