One of my concerns when replacing my 2008 15" MBP with a 13" MBA was whether I could use my old copy of Final Cut Pro 6. I found conflicting opinions on this in the forums, but I went for it anyway.
I simply connected my time machine backup when setting up the MBA and it imported all my old apps correctly, including Final Cut Pro. All I had to do was enter my serial number again and I was up and running.
I haven't done any full projects yet on the MBA, but have played around and everything seems to work fine - and very fast if you put your files on the SSD. I shoot full HD with an XDCAM EX, and the clips all open up with no problem. I tried exporting a HD clip to a 852x480 h.264 file and it was almost twice as fast as my old MBP.
The MBA is not going to give you top performance for video, but it's a big upgrade compared to what I was using before, and the portability is fantastic. I use my old 23" Cinema Display as an external monitor. It would be nice if the MBA supported two external monitors, but it doesn't. I will also miss the firewire port, but it looks like Thunderbolt adaptors are starting to come onto the market, so that should help.