I've had this issue on two textures now, diorite and oak wood.
The edges of my textures turn transparent, I went into the .png files and put a layer of solid color under them to make sure they weren't partially transparent and it hasn't fixed the issue. Does anyone have any idea why this is happening? I'm using a 1.7.10 client with OptiFine 1.7.10 HD B7.
It has to do with mipmapping. If you go into your video settings and turn mipmapping down to 0, does it go away? If so, make sure that all your texture files aren't at an odd resolution, like 31x31 or 63x63. Putting them at even resolutions should fix the problem.