Big DN fan, my thoughts:
1) Only a mistake if you consider his goal to be "kill as many people as possible" rather than "reduce crime as much as possible", and for the latter the small loss of anonymity may well be a justified sacrifice for the deterrent effect he could achieve by exposing his own existence. Especially since, as you point out, he might well have been discovered anyway.
2) Yep, pretty big mistake there.
3) I think you slightly under-rate this one, by not considering that L can't always eliminate people with certainty, prior to this it would have been possible that Kira was not Japanese but was timing his kills to make it look like he was to lead the police awry. This test made that hypothesis a lot less likely.
4) Agreed, this is the big screw-up, also probably the one that most of the viewers could have been expected to spot.
5) Bear in mind he was actually quite careful to prevent Penbar from being singled out, although he could have done better by delaying all the killings for a week or so. Misora would have narrowed down his anonymity even more had she not been killed.
For his optimal strategy, might he not have been even better off by deliberately sending misleading information, by timing the killings to indicate he lived somewhere else for example? After all, applying your strategy might well narrow it down to 'people who know information theory' which probably costs quite a few bits.
I more or less agree with you on point 1. A rational person could have reasoned in that way. But I think we have to say that Light did not. He wanted people to recognize his work when it came to killing apparent criminals because he wanted admiration as a goal in itself. This led to the most obviously avoidable mistake, #3.
I don't know if this is a little too afar field for even a Discussion post, but people seemed to enjoy my previous articles (Girl Scouts financial filings, video game console insurance, philosophy of identity/abortion, & prediction market fees), so...
I recently wrote up an idea that has been bouncing around my head ever since I watched Death Note years ago - can we quantify Light Yagami's mistakes? Which mistake was the greatest? How could one do better? We can shed some light on the matter by examining DN with... basic information theory.
Presented for LessWrong's consideration: Death Note & Anonymity.