Is it possible to re-watch recent matches?
No, unfortunately Battlefield 3 does not have a theater mode. The only way to re-watch them would be if you recorded while playing, such as using a HDMI capture box like the Blackmagic Intensity on a console, or using a screen capture program like Bandicam or Fraps on a PC.
You can review the stats of your recent matches on Battlelog, but this will only show essentially most of the stats that appear at the match summary screen after a match.
Recently, EA announced the release of Battlefield 4 for sometime late in October 2013, which will include a theater mode.