And HTTPS requests are encrypted. The whole request, including the "GET /someurl&password=s33krit HTTP/1.1" part. As I said, using POST doesn't add any additional security to this.
That's why professional security audits will ding you for putting anything sensitive in a URL.
And having read and written this particular audit line item about 29074894389734897 times in the last 15 years, let me assure you that logging is clearly an issue.
The bit about how "if someone can see your logs you're already boned" is also message-board-logic more than reality. Logs are shipped all over the place. On a network pentest, one of the things you do when you pop a box is hunt for logs; even after you get root on the machine, you don't automatically have all the passwords that get stuck in the log files. Same goes for all the random LogLogic-style consoles those logs get fed to.
If you have more questions about this stuff, my contact info is in my profile --- just click my username above this comment. I just wanted to chime in to say that 'carbocation was exactly right, but my comments are now repeating themselves, and so I'm done on this thread.
And POST over HTTPS keeps the POSTed values hidden from those who might listen, whereas with GET over HTTP it would just be out there in the URL.