How to respond to a professor who was insulted by an email detailing mistakes in the exercise?
To me, this is such a non-issue that it doesn't warrant much of a response. So let me add a response :)


  I didn't mean to imply carelessness, and I am sorry if that's how my email came across. I was a bit overzealous in my email. I will address the errors in the skeleton program in my solution, as you have indicated. Thank you for your detailed response!


I think you should take this (very minor) “incident” as a learning experience about how people might perceive your communications. Professors are people; they sometimes make mistakes, they sometimes make pedagogical choices that students don't agree with, and they all take criticism differently.