Lets discuss advantages of going slow.   Beginning of the dive, I like to settle on the sandy bottom and look every diver in the eye for a moment. I learn a lot from that glance.  As you can imagine many are stressed, hurried, or anxious.  Often divers are still getting their gear straightened or figured out. It can take a minute or two to totally relax. And that is really the goal of slowing down.  The most important part of your whole dive is the first 3 minutes. Get your wits about you and relax. 

On the boat. Relax, get your gear ready at a comfortable pace for YOU. Not following someone else or trying to keep up. That is where mistakes are made. Double check your pre dive checklist whether you carry one or it is in your brain.  Help your buddy get ready and you might remember something you forgot with your prep. 

Very important! Don't rush, and don't let someone rush you.  Listen to your breathing. Relax, slow and steady.  Look around you. If with a group, identify the divemaster and make sure your buddy is right there with you. If not then plot your course, where is the beach or boat? Which direction are you heading on your compass? All your gauges working correctly? Octopus readily available? Everything still attached where it should be?

This is obvious stuff but when you are rushed or feel like you need to keep up with others, you can easily make a mistake.  

4000+ dives and I have still forgot to turn on my air or even jumped in without my fins.  My favorite was a friend that jumped in with his glasses still on. It can happen to anybody.  Enjoy.