So if they bypass a tricky part of the dungeon and successfully map it, they can ignore it for the time being? The example that comes to mind is getting past the trapped stairs in the House of the Three Squires when leaving—the characters used a rope to climb down and climbing up is an even harder Dungeoneering test.
This map allows you to move about the wilds and dungeons a bit more freely. No tests are required to travel between two successfully mapped areas.
Of course, when they leave for town and come back, they should expect traps to be reset, if denizens are around to do so.
I think you’ve got the general idea. Once they navigate a hazard and successfully map it, they don’t need to test that hazard again unless it’s nature changes. Now, going one direction along a one-way hazard would not entitle you to navigate it backwards, so they might have to test to climb back up the rope, which they would probably need to do anyway with the high chance they’ll be chased by kobolds on the way out… but I’m not 100% sure on that.
Posts 81–84 in this thread should answer your questions. The cartographer skill acts, in effect, as the dungeoneer’s version of Let it Ride or as Mouse Guard’s Fun Once rule. As long as the map is correct, you just cut from one area to where the players want to go. And, as you note, the dungeon might change after the map was drawn.
Regarding the rope in your example, you could just call it a Good Idea. The interesting bit about the stairs was the trap, after all, and as long as the party doesn’t need to climb that rope in a hurry – persued by a big stone spider, perhaps, or a horde of enraged kobolds – I’d treat the rope as the solution, not the problem.
Of course, if your players want to get that writing desk out of the cellar, a better solution might be called for.
That confirms it. Thanks, Bobo and jovialbard!