Definitely. I'll note if I call a cue early/late. If I'm operating the sound and lights and the company knows that, I'll say something like "LX15 went early today due to operator error." If something wasn't pre-set correctly, I'll note that as well. As was said before; if I'm noting all the mistakes that were made, mine should naturally be included!
I've had one producer say that he found it humorous that I included my own mistakes in the reports, especially since (for that particular company) I was the SM/ASM/Lightboard Op/Soundboard Op. I told him that since I had so many duties, there would be nothing to put in the report if I never noted anything I did, right or wrong.
Having said that, if something was broken before the show/during intermission/what-have-you and it was fixed, I will also note who fixed/replaced it, even if it was me. That way there is always a trail of who did what. Do others do this as well? I like to note the positive along with the errors (a Q sequence that went perfectly due to the efforts of many different parties, a quick prop/costume fix, etc.)