To give specifics It would to depend on exactly what you were planning to get mounted. For instance, on a whitetail deer, which is the most mounted species on the earth, you want to look for well groomed hair, shining eyes that look like they have life in them, also clean crisp ears that look like deer ears, not out of shape with curled over edges.
Another thing to look for is a seam where it was sewn up, even though it is most likely down the back where it would not be seen hanging on the wall, it speaks volumes if it is undetectable. If the taxidermist takes the time to carefully hide the seam, odds are he spent the needed time to correctly do the parts that will show when displayed.
Also learn the animal yourself, everyone thinks they know what a deer or mallard drake looks like when in reality they really don’t. Study the hair and feather patterns, ear shapes, colors or duck feet and bills, etc. This will make it much easier for you to recognize high quality work as soon as you see it.