These artifacts don't matter, since they'll disappear when the texture is mipmapped, which is the whole point of having padding in the first place.
Only annoyance is if you want to show texture flats in a portfolio. Then it might look sloppy to those not in the know. In that case don't use the padding in 3ds Max, do it in Photoshop instead. Solidify filter does a great job, or you can use Xnormal's Dilation filter. http://wiki.polycount.com/wiki/PhotoshopTools#Actions.2C_Filters.2C_Scripts
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Only annoyance is if you want to show texture flats in a portfolio. Then it might look sloppy to those not in the know. In that case don't use the padding in 3ds Max, do it in Photoshop instead. Solidify filter does a great job, or you can use Xnormal's Dilation filter. http://wiki.polycount.com/wiki/PhotoshopTools#Actions.2C_Filters.2C_Scripts