Seems to me like you listed most of them. Another one becomes visible as you get enough rep to see flagged posts, then you get a notification of the number of different types of flags and posts waiting to be reviewed. They can come in a few colors, based on the types of open flags. One more occurs in the chat room, when someone replies to you.
As to whether they're all needed, we need to look at the differences between them.
- The top notification bar can't be missed or ignored, it's disruptive.
It's great for new users, who get new badges and privs fairly
frequently, but they might miss the inbox notification or not
- The red bullet on the inbox and the flag counters are contextual.
They're both not important enough to "abuse the power" of the
disruptive top bar, and they mark things which can be accessed later
using the navigation controls marked by the notification. So they simultaneously alert the user to the updates, and show how these updates can be viewed, but they don't contain the updates themselves, as opposed to the top bar.
- The election notification is site-wide, it's not directed at a specific user. So it can't use any of the first two methods, because we also want it to be persistent and non-dismissable.
- The chatroom notification occurs in a completely different setting and context, and it needs to be very dynamic. It's displayed iPhone style right on the input box, where most of the users' interaction with the chat room takes place.
So of the four kinds, none could really replace any other. The flag counters could possibly be merged with the inbox notification, if the flags arrived through the inbox - but it wouldn't be as efficient, and in any case at the moment they don't.