People don't set out to make mistakes.
Unless you're dealing with a deranged person, people don't set out to make your life harder.
The reason I'm not upset about working late because I caught a mistake that "someone else should have caught" is simple:
This is why we work on teams. We work together, bringing a variety of different strengths to the outcome we seek to create. Together makes our collective work better.
This is *the reason we work on teams.
Together, we will get things corrected and we'll get a clean document that we're proud of to our client.
We can be proud of our work, but more importantly, I think, we can be proud of our team-work.
The buck stops here.