To help you more efficiently, it would be really good to provide some more informations. Like the UV Layout, Material Setup or how you imported the model. For the time being you could check out the following topics on the Crydev Wiki http://freesdk.crydev.net/display/SDKDOC3/Home
This is definitely problem with UV-mapping. UV are too close to texture's borders. What you see is actually first MIP-map, which is half-sized original texture. Increase padding on your texture to leave a place for MIP-maps, this is the only way.
Crytek's technical artist
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Crytek's technical artist