Glad to hear you'd like to add the feature, I'll try and give you as much info as you need :)
There are two types of borders you could add,
1) For icons, just adding an empty border (either black for masked textures, or alpha=0 for alpha textures) around the edges, this is more important for alpha textures doing this will solve the problems in the images above. You probably know this already, but I'll explain anyway ;) The mip-maps are generated in blitz by taking the texture then making it 1/2 the size, this scaling involves a filter to blend the pixels, so if you have a lot of subtextures inside one big texture the edges of these textures will blend together :( So what your seeing the images above, are the edges of the other subtextures next to the one being displayed because its using a mipmap and adding a border will stop this.
2) For repeated tile based textures, the border should be a repeat of the texture edges - as if the texture was repeating for a few pixels at the edges. Its hard to explain this one, without drawing pictures :S
The amount of pixels to make border depends on the size on the texture and the number of mip maps you make - but generally you can get away with adding a 2-pixel border, it's always worked for me :)
There are two types of borders you could add,
1) For icons, just adding an empty border (either black for masked textures, or alpha=0 for alpha textures) around the edges, this is more important for alpha textures doing this will solve the problems in the images above. You probably know this already, but I'll explain anyway ;) The mip-maps are generated in blitz by taking the texture then making it 1/2 the size, this scaling involves a filter to blend the pixels, so if you have a lot of subtextures inside one big texture the edges of these textures will blend together :( So what your seeing the images above, are the edges of the other subtextures next to the one being displayed because its using a mipmap and adding a border will stop this.
2) For repeated tile based textures, the border should be a repeat of the texture edges - as if the texture was repeating for a few pixels at the edges. Its hard to explain this one, without drawing pictures :S
The amount of pixels to make border depends on the size on the texture and the number of mip maps you make - but generally you can get away with adding a 2-pixel border, it's always worked for me :)