Rendering glitch with multiple cubes + aliasing

I have a map of 3D cubes and everything seems good except for two things.

First I have a problem that when I move my VBO of block up and down I get at some places little lines that flicker when I move.

The other problem I have Is about aliasing some textures flicker allot.

I know I can fix this one using linear filter for my texture but the problem is that the linear filter cause texture bleeding since it blend the closest colors together or something like that. glShadeModel(GL_SMOOTH) or changing the pixelformat of LWJGL isnt helping since the problem is texture based and not polygon based.

One last thing, if I change the pixel format for anything else than 0 I get again little lines between my cubes I don’t know if this one I a texture bleeding problem too.
http://postimg.org/image/i3a6bller/

–Ps I dont wan’t to use shaders if possible. I in the range of the possible I don’t want to limit old computers.