Ted,
Most of the island is protected. There are a few places to spear, but it can be hard to find a boat to take you there. THe north side of the island, by Barracuda reef, used to allow spearing and on the Eastern side of the island there was also spearing, as well as at least one sunken galleon that has given up a few gold coins.
A few of my dive buddies have speared down there, but they were on scuba and it was with a small boat that they had been diving with a couple of years in a row. They were spearing up by Barracuda reef and were hitting depths around 160' along the way.
I was also talking to one dive guide who used to do some pretty wild dives up on that end of the island. He would start with a single tank and a lift bag and then dive to 300' and look for black coral. THen, he would get up to his 100' stop and hand off his tank to another diver who would then hand him a new tank and a lobster bag. He would continue to work up through his stops, to 30', collecting as many lobster as he could find. Finally, at 30' he would get switched over to a third tank and be given a speargun- another diver would swim down the extra tanks and take away his old ones, along with the coral, and lobster. For the remainder of his shallow stops, which were the longest on his computer, he would spear as many fish as he could. I guess it was good money, but he later decied ti was a little too risky to do for long.
Cozumel is also famous for it's currents which are something that you have never experienced before. I've been there at least a half dozen times, but stopped going once they put in the golf course. :head
Jon