How to deal with a coauthor who introduces errors This situation has arisen a couple of times for me and I don't know how to deal with it: 

I'm writing a paper that contains formal mathematical statements and proofs. I am very careful about ensuring that my statements are precise and that the proofs are correct. Usually my coauthors are equally careful, but sometimes I have a coauthor who isn't.

The coauthor will edit my careful statements and proofs, presumably with the goal of improving the exposition. But they end up inserting errors, such as dropping necessary assumptions from theorems or incorrectly simplifying something in the proof.

If this happens once or twice, I don't care - it's an honest mistake and they are improving the paper overall - but some people make a habit of it, sometimes to the point where they are more of a hindrance than a help. It really annoys me, as I need to fix their errors and I end up not "trusting" my coauthor - i.e. whenever they make edits I'll go through and check what they've done. 

Here's an example: Essentially, the proof of our main theorem involved defining a function, proving several properties of that function, and then using those properties to bound the integral of the function. My coauthor "simplified" the proof by redefining the function to be the integral of the function I had defined. This meant that the function was now a constant and the rest of the proof made no sense. He obviously had good intentions, but didn't understand the proof he was editing. This error made it into the arxiv version of the paper. It was not a big deal and nobody said anything, but it was annoying, as I had correctly written that proof.

I keep my displeasure in this situation to myself, as I don't want to offend my coauthor or appear unreasonable, but I want to tell my coauthor to be more careful. It's also good for them to improve their work habits. Usually I'll leave a comment for my coauthors in the manuscript explaining why things have to be done this way, but that doesn't seem to get the message across.

Is there some way I can encourage my coauthors to drop this bad habit without offending them?

EDIT: To be clear, I'm talking about coauthors at approximately the same seniority level as myself.

EDIT: In the example, it wasn't just the two of us. There were other more senior authors. So I didn't feel like it was my responsibility to address this issue. I didn't talk to the other authors about it, but one of them did also express irritation.
I recommend two different approaches, depending on the other types of value contributed by your co-author:


If your co-author is not contributing technical value to the project at all, then you don't need to make a big issue of things: just simply do not invite them to collaborate with you on your next paper.
If your co-author is contributing in other areas, but inconsistently for the proofs, I would recommend using a good version control system (e.g., Subversion, mercurial, git).  Then you have an easy mechanism by which you can do explicit review of the changes that they introduce and adopt precisely the ones that you are positively comfortable with.