In modern games, no. Any puzzles that require moving things around are reset by going out of the room and back in. I thought I was stuck in the boulder puzzle in Route 23 of BW2, but I eventually found a way back.
Similarly, even with the season feature in B/W, the season doesn't change until you go inside and back out, so you cannot be stuck anywhere that's only accessible in Winter for example. I'm not 100% sure about Twist Mountain because you go in and outside multiple times, but I'm sure they thought of that.
However, it is supposedly possible to get stuck in Red/Blue by cutting a tree then saving on that spot. When you come back to the game, the tree is back again under your feet and you cannot move off it.