Next packet will be out around GenCon (definitely available at GenCon, may be available online in advance of GenCon, at the same time as GenCon, or shortly after GenCon, they're working out the details). All of the classes have been revised to respond to feedback. They're getting positive feedback on most major core areas, except healing; but healing won't get a big change until after the next packet, due to time constraints.
Clerics will get some free healing, separate from spells.
Hit points will get cut down some, both in terms of PCs' and monsters' hp totals, and in terms of damage done. Should have about the same results, but with smaller numbers and better scaling.
New packet will include character generation rules and cover levels 1-5.
I think that covers the core D&D Next updates. I didn't listen to the Dungeon Command part of the podcast.