On May 22, 2012 Nikon released a minor firmware update for the Nikon D700, which updates section A to 1.03. Meanwhile section B remains 1.02. I updated the firmware of my D700 in short order, since I had run into some of the issues that the update is said to have fixed.
All seemed to be well at first, but last Monday afternoon while shooting I noticed that the camera locked up and showed the low battery warning on the top LCD. That seemed rather odd to me, because the battery was showing 23% charge when I had checked it a few minutes earlier (I wanted to be sure I could finish a bracket set and I knew the charge was getting low). It wasn't overly cool out (16ºC/), so I figured it was a minor glitch. I pulled the battery out, and put it back in, and the camera reported 18% charge left. I switched batteries at that point, so I wouldn't have that problem again.
I shot all day on Saturday (with 8AA Eneloop rechargeable batteries, in the MB-D10) and had no problems at all. The rechargeable batteries got low towards the end of the day, but I hadn't recharged them for several weeks, so that didn't concern me (still doesn't). Yesterday afternoon I was taking some product shots and left the camera for the evening. I came back to the camera later in the evening to find it showing the low battery warning on the top LCD. This time I knew the battery was fine, it is a different battery than the one last week, and it was showing 66% charge after I reinserted it.
Before the 1.03 firmware update I never had this problem with the camera locking up with the low battery warning prematurely. This leads me to believe that the recently released firmware update could have a bug. If any other Nikon D700 users, who updated to the 1.03 firmware, have experienced this problem, when using genuine Nikon EN-EL3e batteries make sure you send a note to Nikon about the issue (and post a comment here). If it is just me, then I'll be taking my camera into the Nikon service centre to get checked out.