Try with a different camera. Same with or without the grip. A different charger. (like Mr. Spokane said: could be the charger). Or the camera cant read the information on the chip (is it a problem in the cam or the charger?) Summary: facts should lead you to the fact, that is common.
I had this painful moment once with the 5d2 and the grip. It was a little bit loose, this blocked the controls on the grip, but not on the body....
I had several cameras, analog, digital. The 5d3 is the worst one in the discipline "exposure to the left". Too conservative. A very small bright spot- a very dark file. (good for high contrast, but .....).
The 1d4 is more honest (?), more intelligent(?). And so is the Sony RX100.
Didnt notice a difference using af- mf, will watch this in the future.
2 times strange things happened: August 12 after a longer burst with the 1D4 and a Sandisk extreme 60mb/s it froze, showed err02, before I could do anything, the message disappeared, no loss. A few days ago: a shorter burst, 5 or 6 frames, it showed err02 again, it changed only after I waited a few seconds, switched the camera off, then on again. The pictures werent on the CF - card, but on the SD- card. The CF was a Transcend 1000x.
I formatted every card I have the first time on the PC too, then in the camera too. Too few days gone, but no issues. I will see.......
Since 30 years I have carried my stuff nearly everywhere. Beaches, mountains, small planes, sailing boats. Never felt unsecure, just thought a few seconds about safety (belt wrapped around my hand, will there be drops of salty water...), but then you should forget this and simply make pictures. Never had a problem.
Make a "Calibration". This means: one time load the battery, till its full, then use it, till the camera shuts down after shots, doesnt matter with or without liveview, making video etc. So the camera "know" the capacity. Then the percentage of remainig power should be more exact.
But- as mentionend before- Lion cells dont like to be loaded full or empty, they like to be between 40 and 80% (loads of information is on the net).