I remember having this issue myself, some time ago. Can't recall how I fixed it but I do know that it was a fairly common problem having to do with Minecraft itself. Optifine actually fixed it for several people, but normally it was a graphics card setting.
http://www.minecraftforum.net/forums/archive/legacy-support/1824238-strange-transparent-borders-on-blocks
Here's an archived page from the Minecraft forums detailing the problem.