The issue here is clearly a charger issue. It is not going to be affected by the cable, so anyone wasting time with that theory... stop. I am an Electrical Engineer and have worked on this type of stuff at the IC level. While I dont know exactly what Samsung has done here, I can make a pretty educated guess. The wall plug has a 'chip' in it. That chip is very specific (in that ALL the ones sold with this phone, and probably most of their phones have the same one). A few manufacturers make them and this is the one Samsung chose to use, and it probably has some programmability - or sends some specific signal to the phone when it is charged. OR it is possible the phone detects something in the charger unit OR the phone sends some acknowledge signal to the charger and if it doesnt receive back a specific signal it dont 'play happy'.
Given the quick-charging nature of the phone, it is likely this is a fairly newer USB chip in the wall unit - and it is a little buggy. But that functionality could also be in the phone, which is also buggy (Samsung is NOT know to make the most quality product - and in fact they are such a bad company that any engineer I know who has ever worked with them refuses to EVER own one of their products... I almost didnt buy this phone because of it, but I still like it better than the current alternatives, so...)
I have had this issue with my 2wk old Skyrocket a few times. Full charge. Let it sit 3 hrs. Dead. Also partial charge and dies very quickly. Also full charge but pull battery and it reads correctly (ie 30% down or whatever). I would expect there to be a fix sometime as this is a pretty big issue, but it is also POSSIBLE there is no simple fix... just depends on how they made the phone. But given a reboot works there should be a simple fix. So I am being patient because as much as this issue REALLY PISSES ME OFF (to the point that I am very close to ditching this phone for an iphone) I am willing to wait it out because I like the phone enough to deal with it.
In any case, it appears that if you charge with the OEM wall-wart, or battery-out reboot, it seems to behave properly. If anyone knows of an app that correctly tells the phone % battery left in the notification area I would very much love to know about it.