Both my brother and a close friend are licensed tree surgeons. One in the UK and one in Sweden... and they amount of training they have had to go through to get certified is stunning - and I've heard a LOT of horror stories.
Another one to look out for is a "barber-chair" scanario, one that is leaning hard before you start to cut, and splits up the grain of the wood the moment you relieve the strain in the back-cut. My brother has a colleague who's helmet was taken off his head by one, and has also lost a colleague to one: his head was flicked off his shoulders in a fraction of a second.
Here's a video of a SLOW barber-chair....
Know your safety zones, and plan your escape routes, and if in doubt,
drop the saw and run.
Falling a tree gone wrong (Barber chair) - YouTube