Ask HN: Can you use Git to deploy software to mass-market end-users?

Hey all, I use Git to manage the development of my software. I have a few thousand users, and every time I release a new version of the software, it breaks in ways I couldn't anticipate beforehand. I have both tests and error reports, but these only help after the fact.

(i) A user experiences a problem, (ii) send me a complaint that explains the issue (iii) I need information to solve the problem (reproduce the environment in which the bug happens) (iv) but I lack the information because the information I need is not present in my environment and I cannot predict beforehand what information will be missing.

To get the required information, I need to talk to the user. But sometimes (often), it's a deep technical problem that is unique to that person's setup. Right now, I build a custom version for the user, that hopefully harvests the required information.

The big problem here is that it's such a long, slow cycle, I want to move on and work on things that are more important than dealing with obscure errors.

So I was thinking, is it possible to use Git to manage debug deployment versions of my software catered to users specifically? I'd build a small interface for the user where she can input a tag/branch and the software will "update" itself to that version.

TL;DR: I need specific information from users to debug obscure errors that are unique to them, can I use Git to deploy custom versions of my software that can fetch that information quickly?

Also, any tips or something from others who're dealing with this would be awesome :)