Broken textures above 32x32.

If I have a texture pack enabled above 32x32, the items start to crack/break. This bug really annoys me and if you can tell me if its my screen resolution or not. I want to know this answer because on YouTube, people with 256x256 or 512x512 have no problem with these texture packs. For example in the image that came with this report, if you zoom in on the textures on the hotbar, the texture is missing but in my hand, the texture is perfectly fine.