I have only been comfortable using my credit unions online bill payment system where the service they use already has the target in the database. When I enter the name of the company and the zip code from the bill, the system responds with the address that matches what is on the bill.
In most cases the money is not sent via mail, but it is sent electronically. This eliminates the case of somebody finding the check. Though electronic delivery doesn't guarantee that I didn't type the wrong account number.
When adding a new target, I like to pick those that also have an online system that I can check in a few days to make sure the money was received and properly credited.
Recently a company failed to credit my account in a timely manner, my credit union actually noticed that the payment hadn't been cashed, and alerted me.
I asked the credit union about mistakes, either by me or by them. They claimed that the payment is treated like any other check, and that if there was a problem the money could be pulled back, and my account credited with the funds.
Your bank should have a disclosure document stating the risks and protections with the service.