The QR code supplied by designer was incorrect. This was discovered by the client after all materials were printed and delivered. Everything was scrapped and reprinted. What level of responsibility does the designer have?
The designer would have to really screw up on their end, not just in design, but in the handling of the project to ever pay for a reprint. Or they'd have to really want to salvage the client and be generous.
Typically, a designer will send a final proof to the client. If the client approves it then the designer no longer has any obligation to fund fixes.
Now this is interesting because you say its a QR code. I imagine this means there was a QR code but it went to the wrong website. If the proof has that same incorrect QR code then the designer while messed up probably doesn't have to pay because the client, or you, approved it.
I will say if its an agency or even a publication and the in-house designer was the one that made the mistake, even if the client signed off, they'll probably be willing to at least offer a discount to keep the client happy.
For a full refund though the designer would've had to make a mistake AFTER the proof was approved. Say approving one version then accidentally running a different one. That doesn't sound like the case here.