For those writers aiming at a daily word target and who won’t leave their Macs 'til they get it, it would be handy to have a word count for words typed that session, ie, since opening the project.
Sure, I can do a little nifty subtraction but something that I can check at a glance would really motivate and/or terrify me.
Keep up the good work.
Scrivener has helped me to see my work in a new way and I can’t thank you enough.
Steve
Norwich, England.
There has been a fair bit of discussion about session targets and word counts in the past, and the reason they got dropped from Scrivener 1.0. I can only say this: 1.02 will be out in a matter of days. 
In the meantime, it seems like one way to do this would be to start the new part as a subdocument of the current document (switching immediately to Edit Scrivenings so you can see where you are). Then you can turn off Edit Scrivenings as you get going, and see your word count of today, then merge the subdocument back into the original. Er, I think there’s a command to do that, but I don’t remember for sure.
Also, as has been pointed out elsewhere, if you select your writing for today and then right (or control) click on it, it will give you the word count of the selection at the bottom of the contextual menu.