Both of these problems are very common because a lot of people leave their Playbook on "stand by" for too long and they drain down too low. The charging circuit is software controlled and if the Playbook gets too low there is not enough power to run the software to allow the Playbook to charge itself. The charging circuit allows for a 10-15 second charge so that the charging software can engage and then stops assuming the software has taken over the charging process. When the Playbook is completely dead, this can't happen, hence the "stacking" trick. It's a pain in the butt, but it works.
Good luck and enjoy your Playbook. I love mine.
Thomas