Minor Plot hole: Rapunzel's hair completely turn brown when she is given a haircut. This however goes again the logic of plants and growth. If you cut a leaf from a plant, it will lose its green color because it is no longer attached to the rest of the plant, but the plant itself does not change color.
Likewise, if Rapunzel's hair get cut, only the detached hair from her head should become brown because the rest is still attached to her head, which is itself the source of her magic (her healing abilities are also transmitted through tears). Thus, when Flynn cut her hair at the end of the movie.....she should have stayed blond.
Plot contrivance: Flynn has a very strong body. He can get hit on the head repeatedly and stay unconscious for a whole day inside a closet without permanent damage. His physical invincibility is however useless versus dagger wounds to the stomach.
Plot contrivance: Flynn and Rapunzel are stuck in a cave quickly filing up with water. Rapunzel uses her magic hair to illuminate the cave in order for Flynn to punch through a rock and let the water and them escape . This means that tons of water were not creating enough pressure to push the rock out of the cave while Flynn's punch (slowed down in water) was enough to do the trick.
Unaddressed Issue: For 18 years, the King and Queen of the Kingdom have been mourning the disappearance of their only girl. It is curious to notice that during those 18 years, the royal couple did not actually get any new child. Which means that if Rapunzel never came back to the castle or was killed, the Royal line would be terminated. Was it their plan ?