This article describes possible reasons for an "Error processing checkout: The zip code you supplied failed Validation" errors

The zip code you supplied failed validation

Why did your customer receive this error?

This error occurs when there is an attempted transaction where the billing zip code provided does not match the zip code on file with the purchaser's bank. This response is received directly from the issuing bank. 

What should I do if a customer receives this zip code error?

If a customer receives this message, they should confirm that their address is current with the issuing bank. If the cardholder has recently moved, it may take their bank a while to have the correct zip code on file for them. If the cardholder hasn't moved recently, they may wish to call their bank and confirm that the information their bank has on file is correct. Using the zip/postal code that the bank has on file for this card will stop this particular error from happening.

Is there anything I can do to reduce zip code errors?

For people that are using Stripe as their payment processor, if the payment is being declined and you'd like to accept it, you may want to see if the “Decline charges that fail zip code validation” setting is on.

You can verify this from the Account Settings page in Stripe. If you're confident accepting payment from this customer when the zip/postal code doesn't match, you may wish to turn that option off temporarily to allow you to accept their payment.