I encountered the same thing too, after a week, I did a factory reset and I don't remember seeing that happen as much anymore. And since the reset, power saving mode is on all the times. Seems to helps a little for me...
I'm getting the switch-on lag too. Seems to be getting worse too. Didn't have this problem earlier. Problem seems to have started since the 2nd firmware update. I don't think a reset would solve the problem because my phone was originally reset and setup as a new phone from day one.
This is a major issue that makes the phone useless especially if we cannot reliably turn it on as and when we need. I didn't have this problem with any of the Notes that I have used in the last 4 years.

