I think there’s one situation where the border was defined by the river but then the river moved, and some Americans ended up on the Mexican side of the river. I’m not sure if this is an active border dispute or not.

I think there are some semi active disputes going about the possibility that some American water management activities in the watershed may cause the river to shift more. For reference, the headwaters of the Rio Grande are deeper into US territory, not on the border

Where the Mexican border ends? The us southern border still exists when not in contact with mexico.