Judith Pinnolis, of the Jewish Music Web Center located a nifty website that she uses to help her type Hebrew: a transliteration tool that creates text that can then be pasted into a standard Hebrew word processor: www.amhaaretz.org/translit.
I found that I cannot paste the text created by this page directly into Dagesh Pro, nor can I paste directly into my HTML editing software (I was hoping to see the Unicode-composed text for HTML purposes), but I =can= paste directly into the ME version of InDesign, and also directly into AbiWord or Hebrew-enabled MS Word. This fact, and the overall design of the transliteration page, lead me to believe that Unicode is being generated. If so, then hebrew text editors will gradually catch up.
In the meantime, the ???? ???? that one sees in some editors (after pasting in the text generated by the transliterator) is an artifact of the fact that Hebrew used to be encoded differently, and is a reminder that the conversion to Unicode, like the move (for Hebrew purposes) to OpenType fonts is eliminating a lot of the twitchy geekiness that has accompanied using Hebrew on computers in the past. And, in the short term, this means that if you are using an editor that doesn't understand Unicode, this tool isn't yet helpful.
Anyway, there is more explanation on the Am Ha-aretz pages, and a great link to David McCreedy's Gallery of Unicode Fonts - Hebrew, so a double bonus of good stuff from Am Ha-aretz' Ami Hertz.