NOTE: I now realize this isn't new, but there isn't anywhere yet that goes very in-depth about it.
While messing around with making a piranha tank, I accidentally burst through the bottom of the tank. I plugged it up quick, but there was still the thin layer of water activating my OCD. Instead of covering and replacing, I noticed an empty cavern below the floor. I decided to just drain it into there, so I popped another block out in the floor to drain it. However instead of draining, the water continuously fell, eventually filling the pocket. Puzzled, I tried to replicate this, and wound up with the third picture in the slideshow.
From my testing so far, a pit 9 blocks wide will be enough to activate the glitch. Any shorter and the water just drains. I am not sure what longer distances will behave like yet, though so far they seem to last a bit longer. I have not timed this, but it does seem that way. Also, only one bucket of water is to be used. If the water is more than half a block tall, it will drain as usual. Another thing to note is that the pit, regardless of size, should be an odd number so you can break the middle block. The closer to the middle the hole is, the longer the effect.
While wearing flippers, you can swim up a waterfall. This may prove a useful means of transportation if someone were to make a more constant design, but for now is limited in how long it is active. Also, it looks like it will only fill up to one block high, then will just flow down with still the same effect. The top of the water may jerk around randomly a bit. Another thing to keep in mind is that since slimes float on water, they can follow you up a waterfall. For the most part, though, this is more likely to be used as a way to have fun and kill time.
I have not tested this in multiplayer at all as of yet.