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Comments
So doing a proper UV map will fix it? (It looks like the whole tail assembly including the twigs and leaf are also bad.)
I'm assuming that I should probably split the problem areas into their own maps rather than trying to throw the whole body/head assembly into all one map?
UVMapper isn't an option for me since I use a Mac, but there are other programs which I could use. UV Layout has a Student and a Hobbyist version which would probably work. There will undoubtedly be other models needing to be mapped if I continue with the project to create models of Oz characters.
You've already got the item fairly well split into materials, which you can select in Hexagon using the Shading Domain panel (default is collapsed on the left) - the only issue I noticed was that one of the ear polygons was in one of the tail groups. You want to map the problem areas along with their neighbours so that everything flows nicely together. Probably cylindrically map the body plus the eyes, and each of the legs, then unfold the ears and inner mouth and do a planar projection for the front and back. I did reinstall Hexagon and have a look at the tools but I can't remember how to use them well enough to do a step-by-step.
You do have a few very non-planar polygons - around the eyes and ears there are a few where the four sided polygon is effectively folded across the middle. Modo hated those, DS and Hexagon seemed to cope more gracefully but you might want to fix them before mapping in order to make sure you don't lose your mapping if you try to edit later.
I'd probably redo the rings around the eyes if I could get Maya to open. But I think my student copy has timed out.
Didn't know about the ear poly having got into the tail group. Will have to fix that. I did know that there's an intersection of a couple of the ear polys between the inner ear and outer ear. Not sure how to fix that without being able to get the program open.
Hexagon should do the job - at the simplest, for the non-planar polygons, just triangulate them (that is, split them in two) - don't triangulate all of the non-planar polygons though, as it pushes the total up and in a lot of cases isn't needed. But a lot of edits in hexagon do kill the UV mapping, which is why you want to do it first and then sort the mapping out.
I'm wondering if it's absolutely necessary for all of the edges to meet up vertex to vertex. It's not an area which is likely to be rigged for any kind of movement.
No, if it doesn't matter to the model then the edges don't need to meet. Note, however, that the applying SubD may open up unwelded edges, as will displacement, and that the smooth shading algorithm will not try to hide unwelded edges.