[bluesquids]

I picked up my first kayak in '01 specifically for spearfishing. I can't think of many problems you'd run into. You'll wanna leash your gun to the yak when not in use, it can fall off easily....just toss it over the side while gearing up....fins can go over the side easily too and they sink like a rock....I put those in a mesh duffle bag in the tank well.
Boat traffic is the biggest thing I worry about. But, you're much better off near a kayak in a thick kelp bed then a shore diver trying to get out there.
Many people will tell you to use the buddy system.....but in our poor visibility you can't see each other so a one up one down is not possible....so you end up diving in opposite directions...you are basically on your own most of the time anyways....personally I do not want to put myself anywhere within the range of a buddies speargun.
You really shouldn't hunt in water deeper than you feel comfortable diving down too in case a fish ties up. This is when a buddy is helpful to spot you and take turns diving on it.
Shallow water blackout should be on your mind ALWAYS, read up on it and dive as safe as possible.