How can this be a "mistake"? They created something that looks like a captcha to fool the client into believing it's an actual captcha. If they did't know how to make a proper captcha it's better to tell the client so someone else does it.
That doesn't excuse the programmer. As a web programmer, it is, to some extent, their job to know when they're out of their league. But second-order knowledge can be a rare skill.
Don't believe me?
Think about how often you see obvious SQL injection problems - the same (lack of!) thought process is responsible for both.