What if a our company wires money to a wrong account, resulting in the recipient receiving interest for several days. When the wire is returned, won't that cause a problem for the inappropriate recipient in that he/she will have a 1099 for a transaction that never was supposed to happen?

they will receive a 1099, but they will also have received the interest income.

Can they request that the interest be returned?

Yes, they can - but this does not appear to be a material transactions, so there would be no reason to do so. Besides, they are probably deserving of some money to cover the inconvenience of dealing with this transaction.