Variant, mistake, or damage? To me a costume card where there's only half or partial material is a damaged card and should be returned. A mistake (or error) is like an upside down piece of film, or an auto card that is unsigned. Those should be returned for corrected cards, OR kept by the owner if they like oddities.
A Variant can only exist if there is a correction, or it is intentional. For example, a costume card can be a variant if the main portion of the costume is White, but there's a thin strip of purple running through it - a purple card would be a variant. An autograph card can be a variant if most cards say "John Smith" but a few say "Love, John Smith" or "

John Smith" A basic card can even be a variant if there was an error, but it was corrected - we had the unfortunate problem of spelling "Amanda Tapping" wrong on a card - we fixed it, so there is a variant version of that card out there - one that says "Amana Tapping" and one that says "Amanda Tapping".
I won't usually "fix" variants - if someone gets that White costume card, they can't return it and ask for the Purple version, or the "Love, John Smith" auto - but I will fix damaged cards and usually fix mistakes too as long as it's within my ability...