Built in mics on almost all "Handy-cam" video recorders are bad. Not only do they pick up wind noise, most will pick up the internal noise the camera makes. Some are better than others, but I haven't found one yet that doesn't pick it up to some degree.
The only real way to combat this is to get an external mic for the camera. There's a host of them out there, again, some better than others. It depends on how much you want to spend. Most of the external shotgun mics have a foam wind screen that comes with them. I recommend a shot gun mic as they tend to reject noise from the rear and the sides of the mic (not totally, but certainly a lot) and lets you concentrate on the subject rather than the extraneous.
Sennheiser, Audio Technica, Sony all make external mics that should work with this. The AT and Sennheiser mics are mounted on the shoe getting the mic away from the camera noise. You can buy or make better wind screens that fit over the stock foam screens.
I'm a firm believer in getting the best sound possibly on my video. For production purposes, sound is half the movie. Post production music mixing with the ambient sound can really add to the drama of a movie. The better ambient sound you have to work with, the better off you will be.
-- John
