When you're an examiner, making a mistake will usually cost you time, and probably counts. It also generally costs the applicant time and money.
When I first began examining, and found that I had made a mistake in an action, my first inclination was to apologize for it in the subsequent action.
Being new, though, I had no idea whether such a thing was appropriate, or a good idea.
So I asked around, and the general consensus was that you didn't want to apologize for a mistake in an action ['on the record'], because all that would do is call attention to the fact that you screwed something up. Better to just fix the mistake and leave it at that.
There were still times that I really thought that I should apologize, but I continued to follow the guidance I'd received as a new examiner.
There eventually did come a time (after I got partial signatory authority) that I decided that there really were mistakes for which the attorney (or more importantly, the applicant) deserved an apology. These days when that happens, I give one to them.
Most of those mistakes are fairly innocuous, like forgetting to include the initialed 1449 from an IDS with an action (although IDSs are getting tracked more closely these days, so it is harder for that to happen).
Mistakes can be more serious, though. There is one instance that I particularly remember. Without going into the details, I made a mistake that gave the attorney the impression that I was willing to allow a group of claims when that wasn't actually the case. When the amendment came back, the attorney had placed the claims in what they clearly expected to be condition for allowance.
While I was reviewing the amendment, I discovered my mistake.
I felt bad about it, but I didn't have any choice as to handling this situation. It's not like I could allow claims that were clearly (to me) non-patentable. I fixed the mistake, wrote up another rejection and mailed it out.
And I included an apology in the action.
There are other instances where I really would like to apologize, but I don't, because I don't think one is really warranted. One example of this is when I am doing a follow-up search and come across a really good piece of art that I think I should probably have found the first time around. But searching is a subjective art, and you're not always going to find the best art the first time around. Sometimes upon reflection you think of a searching strategy that hadn't occurred to you before. It happens.
Another instance where I get the urge to issue an apology has to do with 101 rejections. For a while, the guidance that we were receiving on the interpretation of 101 was, um, evolving.
I'd send out a 101 rejection, and by the time the amendment came back, the Office's position on 101 interpretation had changed. "Thanks for making those changes for me, but things have changed and now you'll have to do these other things to satisfy the requirements for statutory subject matter." Once again, I feel bad about it, but in this case I'm just following the guidance of the Office, who is just following the guidance of the courts (and I'm getting stuck writing a second non-final for it). It feels like I should include an apology with the action, but under those circumstances I don't think it's called for.
Luckily, 101 has settled down for the time being, so I'm not put in that position very often these days (although with the cases that are currently working their way through the courts, it's possible that will change again soon).
I can't ever remember seeing anything resembling an apology in correspondence from attorneys. That could be because all of the attorneys I deal with are true professionals and don't make mistakes.
It could also be that when an attorney makes a mistake, they probably owe that apology to their client, not to me.
In any event, it's not uncommon to see an applicant change attorneys over the course of prosecution, so certainly mistakes do get made. It only makes sense; nobody out there is perfect.