What kind of silly mistakes have they tried to pin on your team?

Rookie stuff from developers that have never worked in a large enterprise scale IT environment. Hard coding endpoints to other services in code files instead of configs is a big one that comes up far more often than it should. So we'll move code from a dev environment that they own, to one of our QA or client testing environments that my team owns, and we'll wonder why a service call isn't working. We look into the code and find a Dev URL in the code, instead of making it a configurable entry that my team would manage from environment to environment.

Also every time there is a sev (outtage, slowness, whatever) they try to blame it on us, even if it's the day after a code change in that environment! It will work fine Friday, we deploy code on a Sunday, Monday everything is broke and it's finger pointing at my team that we did something wrong. My team has an amazing track record and rarely makes mistakes (that's our job, we're "the gatekeepers"), it ALWAYS ends in them eventually realizing there is crap in their code or it's memory leaking, and we do a rolling hotfix of new code they send up and the issue magically goes away.

I don't care that people make mistakes, but my company has a very conflict centric culture at times, and between certain teams the communication is less than great. Mistakes are fine, just admit to it. When we do make mistakes which are extremely rare, we own up to it and fix it. One team one dream.