Can confirm this is most likely NOT a driver issue, I have an nVidia GTS 450 with graphics driver version 346.47.
This is called UV bleeding... properly sized blocks and items pull the very edge texture, in the cases shown in your screenshots that is transparent. However, if the pixels just outside the used textures are very different (like bright red) it is very noticeable.
So no, this is not a resource pack problem, but one with the model system. UV bleeding occurs by default on even precise models, the only way to fix it is to shrink UV coords very slightly or to surround your texture with a bleed area so when pixel bleeding occurs, it pulls the color from there so it's the right color.
Also gaps in the textures of sign text - some letters and characters mean that there are gaps that you can see through. Don't have time to send screenshot today, might do tomorrow.
Please switch to the default resource pack and see if it occurs there.