How rare is this error?

[swarmee]

Yes. They can put a request in to have PSA log it as a new variation, but PSA normally won't unless it the set has been fully checklisted with the variations in a card catalog or price guide like Beckett or the Standard Catalog. So really, the first step should be to get it officially checklisted. Once that's done, you've got to work with PSA to have them declare it a variation they check for.
I have a couple that I've had graded hoping to get them checklisted over time, then resend in for reslabbing once they've made that variation:
1972 Topps McNertney with yellow fingerprint

1963 Topps Bob Veale with blue and purple streak in sky
1960 Topps Master & Mentor Mays/Rigney with extra brown box on back
There are also two 1967 Laughlin Mickey Mantle cards (one with black spot on pants)

I think all these are in the Show me your print defects thread.

[lowpopper]

@swarmee

I have the Bob Veale "UFO" card in my ebay store

[swarmee]

Thanks; I bought a couple of copies already on COMC. If PSA recognizes it, it will definitely increase in value.

[swarmee]

*double post*

[savedfrommyspokes]

I have seen, and know of multiple other copies of the Juan card (thanks to this thread). However, I have handled many more copies of this 68 Perez card, but have never seen one with this back:

Possibly rarer than the 67 Juan .