This is just a small demonstration as there are many things that classify a pelt as a wallhanger/not-mountable. Most often I look specifically for those pelts with damage to the head that would otherwise render it not mountable for Spooks and reference for art.

Top left: Enlarged eyeholes. Enlarged eyeholes are often stretched/torn eye areas that will commonly lack eyelid material. Both lid material and the correct size hole are required for a proper mount. Almost all times that a novice attempts to mount a fox with enlarged eye holes, the end results in something resembling Kroenen from Hell Boy. Wide eyed, terrified, and just plain horrific.

Top right: Little to no lip matter and slipped/missing fur. While a skilled taxidermist can flock fur or replace missing patches, a head form needs lower and upper lip to secure the skin to the form, giving the proper mouth line.

Bottom left: Slipped/rubbed nose. If a pelt has this, means you'd best reach for a fake nose as this one cannot be saved. Slipping and rubbing occurs at the tannery, perhaps from the result from a poor skinning job, that area not getting enough tanning solution. etc.

Bottom right: Torn fur. While this can usually be sewn or if fur is missing, fur can be substituted in, most often times unless you are familiar with what you are doing, the result will look a bit Frankensteined.

This is by no means all that can classify a pelt, but just some more common findings. If your pelt has one or more of these don't attempt to mount it. If a taxidermist refuses to mount them, in what way does that say "mount me :D".

Save up, get a squirrel mounting kit or two (they're like.. $40 for EVERYTHING) and practice on those before purchasing a taxidermy quality pelt. Practice sculpting eyelids out of modelling clay, get tons of ref pictures. Get a couple coyote capes and do some shoulder mounts even. Once you've got the hang of it and are confident, get the proper supplies for the upcoming job, find the right pelt for you, and go for it. The result will be far more amazing and you will get appraised for your long hard work!