As with any physical activity, video taping yourself allows you the opportunity to gather valuable feedback by dissecting stages of the skill you're trying to perform.
In the example of snowboarding, you can watch your take off, your landing, your control in the air, etc. This gives you an idea of what you are doing, what you should be doing, and what you can do to bridge this gap.
I think a vantage point perpendicular to your path of movement will provide you the best angle for analyzing.
I used video once when I first started doing mid-sized kickers. I was having trouble leaning backwards too much after take off, getting height without losing too much forward momentum, and orienting the board under my body appropriately for landing.
Watching a video of me doing a couple airs allowed me to gather incredibly specific feedback and quickly address the issues preventing me from mastering the skill.
Always be careful with the equipment on the hill, and the cameraman must be aware of his position in relation to riders on the hill at all times.