If God can do anything can he make a mistake?

Apparently that applies to religion as well, otherwise God would be able to do some pretty nonsensical things, and by nonsensical I don't mean things that may not make sense to us (yet or ever); I mean things that don't make sense, period. And if that's the case, then literally anything that follows "can God" is possible. He could make himself not exist without ever being nonexistent, he could slaughter with benevolence, he could both grant and deny requests with and without reason, and he could make a mistake without compromising his perfection. I'd bet he could even do things that he himself can't do. Sounds like crazy talk to me, but that's the premise. So...