slight problem (spoilers happened round about episode 20)

[Kanokonfan]

I can't remember which exact episode it was but I was thinking about when Light tried to tell L that he may be Kira and be unaware of it. L didn't believe him obviously thinking Light was hoping to not be punished after convincing people he was unaware of himself being Kira.
The problem I have with this is the tapes that Misa sent in that claimed to be Kira and proved it by killing news reporters right after telling people to change their channels over to see them die. Wouldn't the tapes have proved that Kira was aware that he/she was Kira?

[MaruDashi]

He believed that the person who sent in the tapes was a second Kira, one who had different powers than the first Kira. So, he believed that perhaps the Kira had powers and didnt know it, and the second Kira could kill with just looking at their face/without a name.