I spoke with a very helpful customer service agent at Marriott Rewards and he cleared up my questions. Here's the information I got:

Qualification for a new elite level is by "rolling year." In other words, to make Platinum, I have to have stayed 75 days in the past year, and stays "fall off" 365 days after they have been posted.

Qualification for an existing elite level are done by year to date. In other words, once you qualify for Platinum (or Gold, or Silver) level, the date you qualified becomes your elite renewal date and you will be renewed as long as you have 75 (or 50, or 25) days since that date.

Weren't those the same rules they had for elite qualification under the old program?

The only difference is that stays at Courtyards, Residence Inns, and other properties also count towards elite (which is a nice change).

The "rolling year" thing is so byzantine - who can remember what your stays were over the last 365 days? I guess it's time to start logging them...

Rudi: If you were Gold in the old program, you're Silver in the new one. If you were Black in the old one, you're Gold in the new one. (Platinum is still Platinum.) If you are gold or platinum, you are entitled to concierge level access and room upgrades under the new program. (Although in my experience, upgrades are difficult to come by at Marriott black (now gold) level.)