Personally, I'd be looking elsewhere for the cause of your softness (after making sure the filters were clean, of course).

Good quality coated filters do indeed add more air-to-glass surfaces, but the effect is not only negligible, but no different than switching from a 4-element to an 8-element lens... While I will certainly grant the point to Drew and others that adding a filter to a given lens will affect image contrast in the shadows and maybe sharpness to an extent, I would imagine that there are more quality variances between the myriad of different taking lenses out there than would be introduced by adding a quality, coated filter.

And, there certainly should not be any difference in sharpness between shots taken with different color, but similar quality, filters.

Camera/subject movement, poor focus, poor scanning, etc. all seem to me to be more likely culprits.

FWIW, I've never heard anyone say anything like, "Oh, that 16x20 print is a bit unsharp; the photographer must have been using a filter!"

Best,

Doremus