Ok, here's how to download the 1280x720 video. Keep in mind that it's a bit over 900MB. First go here:
http://www.videohelp.com/tools/RTMPDump. Download the 2.4 2011-09-25 (September 29, 2011) version of RTMPDump. Follow the instructions posted on that page. Use this stream url:
rtmpe://viacomnickstrmfs.fplive.net/viacomnickstrm/gsp.egvrenditions/nick.com/2012/03/23/09/49/Korra-Eps-101_102-for-KorraNation-sneak-on-3-24-2012-ONLY-ProRes_1280x720_3500_h32.mp4. In the instructions it says to have the downloaded file end in flv but, I chose mp4 and it plays fine in VLC. So, in the command prompt, you want to enter something like this:
"C:\rtmpdump" -r "rtmpe://viacomnickstrmfs.fplive.net/viacomnickstrm/gsp.egvrenditions/nick.com/2012/03/23/09/49/Korra-Eps-101_102-for-KorraNation-sneak-on-3-24-2012-ONLY-ProRes_1280x720_3500_h32.mp4" -o "C:\korra.mp4"
The location of rtmpdump, the output location and file format (mp4 or flv) will be different if you choose it to be.