I have a Series 1981 One dollar banknote graded by PCGS Choice 55 for trade for US or Spanish coins. The attached pictures show the bill I have for trade.
I have not had it appraised by anyone. Several people have offered $25 to $125 when the note was ungraded. Now I would anticipate it to be worth more. As glorkar said "Whatever someone is willing to pay".
I have not seen another note like this for sale, so have not established a "price" for it.
Paper Money of the United States, 20th addition, shows this type of error note to be worth between $125 to $250. Depending on condition. It does not differentiate the different types of offset errors, i.e. light ink, partial ink, complete ink, alignment of offset print, etc.
It's a pretty nice example for this error. Nice that it's graded too, 55's not bad.
Errors are hard to grade and attach a price to. So many varieties exist. Paper folded, butterfly/misaligned cutting, partial overprint, missing/non-matching serial numbers, the list goes on. It all comes down to what someone would be willing to pay for it, not everyone is into errors.
I'd put the value at about $150-$175. If it was a top grade of 70, I can see the $250. Someone else may chime in with another value, no problem.