If it's groove wear you can usually see it as greying or dulling, either in patches or all over. Sometimes it's obvious, others it's more apparent in certain light, or when the surface is viewed from a slight angle. Obviously having said that it's not so easy to see on a very scuffy record compared to a glossy one.
Maybe not applicable in this case, but another thing to bear in mind, is that some jukeboxes played the 45 in a vertical position causing more wear on one side of the groove than the other. Add to this that the stylus on such a jukebox will be prone to more wear on one side than the other, which in turn could lead to it damaging even the lesser played singles in there. This can be one, but not the only, cause for distortion in 1 channel only on a record which is otherwise clean with good gloss.
As has been mention in post #8, playing a mono record in mono rather than stereo can help a lot.