Liking this a lot more, but I think the biggest problem I have with it is that it just doesn't have a very good flow. It animates wonderful, but it doesn't flow as though it is water; this is more noticeable on the edges. For example, the foremost edge of the water looks like it is jumping rather than waves flowing. It seems to work better on the diagonals of the tiles, however. I think it'd work very well if you made the edges flow with a nice steady pattern/sync, that way when you tile them the water actually flows around the whole body of water.
I wouldn't fret about the sides, though. But if you're that worried maybe light streaks or something? There's not much you can do with that small of a cut-out of water to portray what's underneath.