Java 8 Update 131, Java SE Development Kit 7 Update 4, Java FX 2.1.0 SDK , Java FX 2.1.1, Windows Vista Home Premium 64 Bit with Service Pack 2, Intel (R) Core(TM) i7 CPU, 920 @ 2.67 GHz, 6 GB RAM
Video of the end result of the glitch: https://www.youtube.com/watch?v=t-uE-yTCxi8
UPDATE: Video of glitch occuring: https://www.youtube.com/watch?v=jf40ErfAxAY
Basically, an Iron Golem will walk upto the lightpost in the village, take a right and walk right into the water. Unlike when pushing an Iron Golem into the water, the Iron Golem this way starts floating and spinning, as if trapped in a whirlpool.
Note when I nudge the Iron Golem at 01:25 in the first video, it bobs slightly while moving, as if he is swimming and then goes back to spinning.
Video of two Iron Golems spinning with Party Parrots: https://www.youtube.com/watch?v=PPkNeBeIHb8