I'm not quite sure -- but it almost sounds like you have line ghosting. You may want to give this a read and let me know if that's what you're dealing with or not:
The reason for this is due to how the texture image was authored, combined with the filtering that most 3d engines use when textures are displayed at different sizes on screen.
Your image may have coloured areas which are completely opaque, coloured areas which are partially transparent, and areas which are completely transparent. However, the areas where your alpha channel is completely transparent (0% opacity) actually still have a colour value too. In PNGs (or at least, the way Photoshop exports PNGs) seems to default to using white for the completely transparent pixels. With other formats or editors, this may be black. Both are equally undesirable when it comes to use in a 3d engine.
You may think, "why is the white colour a problem if it's completely transparent?". The problem occurs because when your texture appears on screen, it's usually either upscaled or downscaled depending whether the pixels in the texture's image are appearing larger or smaller than actual size. For the downsizing, a series of downscaled versions get created during import. These downscaled versions get used when the texture is displayed at smaller sizes or steeper angles in relation to the view, and is intended to improve visual quality and make rendering faster. This process is called "mip-mapping" - read more about mip-mapping here. For upscaling, simple bilinear interpolation is normally used.
The scaled versions are usually created using simple bilinear interpolation, which means that the transparent pixels are mixed with the neighbouring visible pixels. With the mipmaps, for each smaller level, the problem with the invisible mixing with the visible pixel colours increases (with the result that your nasty white edges become more apparent at further distances away).
The solution is to ensure that these completely transparent pixels have a colour value which matches their neighbouring visible pixels, so that when the interpolation occurs, the colour 'bleed' from the invisible pixels is of the appropriate colour.
To solve this (in Photoshop) I always use the free "Solidify" tool from the Flaming Pear Free Plugins pack, like this:
Download and install the Flaming Pear "Free Plugins" pack (near the bottom of that list)
Open your PNG in photoshop.
Go to Select -> Load Selection and click OK.
Go to Select -> Save Selection and click OK. This will create a new alpha channel.
Now Deselect all (Ctrl-D or Cmd-D)
Select Filter -> Flaming Pear -> Solidify B
Your image will now appear to be entirely made of solid colour, with no transparent areas, however your transparency information is now stored in an explicit alpha channel, which you can view and edit by selecting it in the channels palette.
Now re-save your image, and you should find your white fuzzies have dissappeared!
Source: http://answers.unity3d.com/questions/10302/messy-alpha-problem-white-around-edges.html