Is it considered better to record a long continous video of the whole flight and then edit the pieces you're going to use,  or to shoot short clips while flying (stop/start record mid-flight)?  

If you film continuously you'll just need to make sure you have big enough SD card and be aware the clips are chunked into 4gb files so you may have the section you want across two files that you'll need to merge.

I think continuously! Today, a large SD card is not a problem

By pressing the button you can skip the brightest moments

I've always just let the camera run during a flight and then do all the editing later. That way you can focus on flying and getting all the best angles of your subject. If you do the start/stop option you run the risk of forgetting if you started it and run the risk of missing a great shot.

I always worry that if I only have one long file and it becomes corrupted I could loose the entire shoot. I might run continuously, but I prefer to break the files up when I have a successful take for peace of mind

I prefer the video so I can always speed it up as needed. Single shots can be odd with wind.

Cavu Films Posted at 3-16 08:32
I've always just let the camera run during a flight and then do all the editing later. That way you can focus on flying and getting all the best angles of your subject. If you do the start/stop option you run the risk of forgetting if you started it and run the risk of missing a great shot.

Yep very true I have started and stopped and forgot to start again.AAAAAAAAAAAARRRRRRRRggggggg