Update by Oval:
Since the new swimming animation, you can clip through the lily pads by sprinting, so you aren't getting stuck anymore. To reproduce: place some lily pads on water, and swim through the lily pads.
When you swim in water and rise back to the surface while a lily pad is on top of you, you can pass through the lily pad and stay on the level between air and the water. However, you are not able to go on the surface of the lily pad. Instead, you need to go next to it and jump onto it.
If this description is not clear enough, please edit it.