Originally posted by dms I don't think this is correct--as regards filters with only a single side coated. I believe it is reflections off the lens front element that cause the problem, and thus the filter side facing the lens is the important one as regards presence or absence of coating.
It really doesn't matter which way an uncoated side is facing - reflections from that uncoated surface are the same regardless of the direction the light comes. One way, the reflections have to go through a layer of glass and the other way they don't but the reflections are a function of the air-glass interface and don't care which is first or second.
If you take a piece of window glass (uncoated) and observe the reflections (actually two - one from each air-glass surface), then flip the glass around, nothing will change - same with a filter. The surface producing the noticeable reflections (uncoated side) will move a bit further away, but it will do the same thing reflection-wise. Reflections from front mounted filters would be a non-issue if it weren't for the reflection of the lens elements that follow which can bounce light back toward the filter. Otherwise, the only reflections from the filter would be away from the lens & camera, and wouldn't do anything. Inter-lens/filter reflections are what causes halos, ghosting, etc. (along with a few other things like reflections off iris blades etc,).
Another reason for coating lenses and filters is to enhance their transmission of light. Any light reflected cuts down on what goes through the lens - for regular window glass, that can be 10% or more. When reflection is reduced, transmission increases by a like amount. Again, however, there is no advantage here based on which side is coated; 90% one way - 90% flipped.