I experienced a glitch while on the crossroads swordfight zone. I only experienced it once, and thankfully I had a very recent saved game to go back.
After beating the swordfight and talking with Morgan, I exit the upper part by double-clicking on the exit. Then, I had the animation of Guybrush sliding down on the mast, but when I should have control of the game again, the camera was stuck on the upper part, with Morgan. I could see the pointer cross, but no hotspot to use it, and if I used WASD I actually walked (I couldn't see Guybrus, but I could hear his footsteps).
After reloading the saved game, I exited the zone only clicking, and there was no glitch.
Reloading again, I tried again the double-click, and there's again no glitch.