I want to thank everyone who responded. From the title of the original post to the end on the post I took full responsibility for the dive. How I forgot a simple dive watch can be attributed to my lack of experience despite having dove over the last 25 years. When you are in the water more often than I am the pre-dive check list may seem second nature but in my case I simply overlooked a fundamental basic. Even though the DM timed our previous safety stops my brain didn't click on this very basic AND CHEAP item until the DM wasn't there.
What we did after this dive hasn't been discussed. First, I asked for and received a Dive Computer for our subsequent dives. Next, I asked for and received a Dive Briefing from the DM prior to our next dive for both me as well as my nephew. For my nephew's benefit (I was already kicking myself over my mistakes) I asked the DM to go over everything he felt that we did right, everything either of us did wrong and everything each of us needed to improve upon.
We were a group of four divers, the other two divers were our travel companions. There were no other divers on our boat the day we went spear fishing on the north end of Cozumel. What would I want from the DM in this circumstance in the future? I'd want him to leave his spear gun in the boat and pay closer attention to the divers. I cannot defend my mistakes, I made them, I own them, I am thankful I didn't cost anyone else to have to pay for them.
One post stated what a DM's job wasn't (babysitting). I thought I would grab a few key items from PADI's website on what someone would learn if they took the DM course;
Leadership Skills
Organize
Solve Problems
Help Others Improve
Supervise
Guide
Teach
Our DM did those things and more. Did the dive shop let us down? Yes. How? The DS loaded all the equipment on the boat in a large pile. Not until you reach the dive site were we provided our equipment. On one trip out the equipment missing was a snorkel. How hard is it to set up four divers? Who is at fault here? Still me. What will I be doing about it? Taking my nephew diving again but this time we will bring every item of our own, take it to the boat ourselves in the morning, take it off the boat at the end of the dive, clean it, inspect it and haul it to our room until the morning when we will start all over again. Plus, to make it easier I will have a new laminated checklist attached to my BC.
My post is a cautionary post, though I have many years of experience I am still a recreational diver and expecting the next DM or DS to live up to those I have experienced in the past is foolhardy at best.
I would like to thank each poster, each of your comments are respected and in most cases have caused me to add your comments and suggestions to my thought process. I would also like to thank ScubaBoard.com for providing this website as I will utilize it to become a better recreational diver.