To protect yourself with a sword comes this bug in the textures of the joints of the sword
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You mean the white pixels/textures not lining up?
Yes
This actually happens with all tools.
If I was thinking but I noticed in detail with the other tools
The white pixels can be seen everywhere in the game. For example on the edges and corners of blocks. This is very rare and depends on your graphics card and on the distance and angle you are looking from. There is not much Mojang can do to prevent this because it is, as I said, mainly a graphics card issue. I think this should be closed in favor of other, a lot more annoying graphics card issues like MC-220.

Since most of the blocks don't show gaps at the corners I assume that's not a graphics card issue. Maybe the models of the items and blocks showing this effect are not properly defined or there may be rounding errors / floating point resolution effects. See [MC-2203]
I checked and I can confirm this for several blocks and items. From what I see this is not a graphics card issue. This is an issue with some of the faces of the 3D models not properly aligned. Such white or otherwise wrong colored dots or pixels can bee seen at:
Cannot reproduce in 13w06a.

Can still reproduce in 13w06a

Resolved as duplicate of MC-1794