I found a solution to this problem. It may not work for everybody, but downloading and patching Minecraft with the program MCPatcher fixed minecraft completely and erased all remnants of this bug. For more information on this program, search MCPatcher in Google, Youtube, or some other source of information.
@Kumasasa it was fixed in 0.8, but has returned in 1.7. It's a rather annoying bug, as it is a bug whether it is intended or not, to see moving water next to transparent blocks. I think that it should just work normally, except without the flow animations.