We're having the same issue.  Our Samsung Galaxy Note 10.1 GT-N8013 16GB (White) won't charge from the AC/USB adapter but it will charge when connected to a PC via USB.  When charging from the AC power brick, the battery icon at the bottom right of the screen shows a lightning bolt and indicates that it is charging.   It sometimes works after the tablet has been charging from the PC/USB first -- then for some reason you can charge via the AC power / USB brick adapter.   When charging from the PC/USB port, there is a red "X" on the batter icon in the lower right portion of the screen.   It seems to me that the issue is with the AC mode charging.   I suspect the issue is somewhere in the OS rather than the physical AC/USB power brick itself.
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We're having the same issue.  Our Samsung Galaxy Note 10.1 GT-N8013 16GB (White) won't charge from the AC/USB adapter but it will charge when connected to a PC via USB.  When charging from the AC power brick, the battery icon at the bottom right of the screen shows a lightning bolt and indicates that it is charging.   It sometimes works after the tablet has been charging from the PC/USB first -- then for some reason you can charge via the AC power / USB brick adapter.   When charging from the PC/USB port, there is a red "X" on the batter icon in the lower right portion of the screen.   It seems to me that the issue is with the AC mode charging.   I suspect the issue is somewhere in the OS rather than the physical AC/USB power brick itself.   We're running Jelly Bean 4.1.2 currently.