It's a week late, but the online version of now has BBC HD content today (Monday). Not everything's there (a cursory glance found that No. 1 Ladies Detective Agency was in HD but Mad Men and the recent Doctor Who special weren't) but it's a start. Picture quality on the streaming service wasn't ideal on my (2omb) connection but an improvement on the regular and higher quality streams. I'd expect the download version to be better - certainly I wouldn't want to watch the streaming versions on an 8mb or slower connection.
Two interesting blog posts on the BBC site: BBC iPlayer goes HD, adds higher quality streams, releases iPlayer Desktop out of Labs and BBC HD: Joining the BBC iPlayer family