Since there is no simple way in survival mode to change Grass Path blocks back into normal grass, I find it easiest to turn the Grass Path block into a Farmland block first with a hoe and then trample it and let a Grass block regrow.

To recreate the bug: Stand on top of a Grass Path block and then use a Hoe directly underneath yourself to turn it into a Farmland block.

Symptoms:

• Rapid up and down movement that doesn't stop until you move off the block. Going into "F3" shows actual changes in height. Taking multiple screenshots so as to actually see the numbers reveals that it vacillates between the numbers xx.85910 and xx.93750 (Grass Path height).
  • Trying to walk off the block is very slow (similar to sneaking on a Soul Sand block).
  • Running off the block doesn't work.
  • Jumping doesn't work either.
• Trying to move to an adjacent block that is higher by any margin is impossible. For example, you cannot move to adjacent Grass blocks or other Farmland blocks, not even if the Farmland block you are standing on has turned back to dirt on its own.
• The block acts normally when walking back on it afterwards.
• Quitting the game while experiencing the issue and then reentering the game does not stop the problem.

Probable cause: Difference in elevation between Farmland blocks and Grass Path blocks. They are visually similar in height but when standing on them the Farmland block is higher, being the same height as Grass blocks while the Grass Path block is slightly shorter.

I haven't tested for the problem with any previous versions.
Now tested: affects all 1.9 versions and the first snapshot containing the Grass Path feature.