I would think the authoritative source for TSBs would be GM's service.gm.com site. That lists 15 for the HHR describing technical issues, the most recent being issued April 3, 2006. This includes things like removing rail dust embedded in the paint (which can happen if the car is stored near a rail yard or ore processing plant), clicking hub caps and freezing door latches, which are rare and/or minor issues. As others have said, though, you can't go by that for a measure of reliability.
I think the drum brake thing mostly comes down to looks. I think a vehicle like that should have disks for that reason, but in terms of stopping power, pedal feel and longevity, drums are perfectly acceptable. Most people don't do their own brakes, so ease of service isn't a big factor. Even for those who do their own, like me, once you learn how, they're all the same, so it's no big deal.