1. Dear Direct Report: Please go back and read the original e-mail you sent me regarding vacation time (as it's obvious you did not proofread it before you sent it). Note that my response was entirely correct, given that you a)simply said "a half day left" rather than "a half day left after the request I just sent to you", and b) were entirely wrong on your explanation of our vacation policy. I was very polite about it, and in the end concured that you did have a full day of vacation left, prior to the half day you just requested.
Please go back and read that response, as you obviously did not read it before replying. If you had, you would have realized I was agreeing with you, that after the current request, you still had a little bit of time available for this year. There was no need to reply with a list of the days you've taken, particularly in the tone you took. Remember, I still have some influence over your evaluations.
2. Dear colleague in another department: I called you rather than e-mailing in order to clear up confusion over the five e-mails and three sets of documents you sent regarding an "error" you made that needed to be fixed, because I discovered that according to those documents, what you told me happened was not, in fact, what actually happened. Based on what you told me, the error would have been corrected - in such a way that it made the matter worse.
I've offered several times to have you over here to look at how the information from your system flows through the financial system, in order for you to get a better grasp of the impact of various types of errors, and the process needed to correct them appropriately. You keep putting it off; perhaps now would be a good time to meet?