How exactly are you selecting the areas to be transparent? If you're just using the magic wand tool to select an area, try increasing the tolerance so that it gets the stuff where your texture bleeds into your blank space. You can also right click and select Grow on your selected area to grow it by a few pixels, hopefully eliminating some of the effect. The best way however would be to paint the area out by hand.
In the future, when you're making a new texture to be transparent, it helps to make the background a color similar to that of the main texture so that the borders are not as visible if they are present. This is done most easily by duplicating the texture layer, applying a light guasian blur, and putting it below the texture proper. This way the halo is the same relative color as the texture, and therefore not as noticeable.
Hope that helps