It's great you're thinking about these things.
In the two years I've been doing this, and reading accident reports, it's seemed pretty clear that most accidents are not the result of any one thing, but a cascade of issues, any one of which could have been avoided or solved and aborted the sequence. And the final common denominator is often panic.
As I analyze it, issues with diving can be divided into three types: Equipment malfunctions, human errors, and environmental problems. Sometimes you have more than one operating at the same time.
Serious equipment malfunctions are happily rare. Scuba regulators are pretty simple, and if well cared-for, tend to work well. BCs can develop leaks, but they're usually small and manageable, if the diver keeps his head about him. And they can often be detected before the dive actually begins. In our waters, freeflows are probably the most likely major equipment malfunction we're going to run into, and a diver should feel comfortable with a procedure for coping with a freeflow, whether that's breathing off the free-flowing reg and ascending, or initiating an air-share with a buddy and shutting down the valve. As with many issues in diving, it's much better to have a procedure in place and practiced than to try to figure out what to do when you face something, unprepared.
Much more common are equipment "malfunctions" due to not assembling things correctly or, for example, not turning on one's air. These will be picked up if a really good, thorough buddy check is done before the dive. I can't tell you how many times we've caught somebody with a dry suit inflator hose not connected! It's easy to get complacent about checks, especially if the people around you aren't doing them. But it only takes a couple of minutes to run through everything, head to toe, and it saves a lot of grief. One thing you may or may not have been taught is a bubble check at the beginning of the dive -- This is where you'll catch the leaking BC, or an inflator hose that isn't snapped on all the way.
Masks are one piece of equipment that can fail to function properly pretty easily, and I think all divers ought to be comfortable with a flooded mask, with removing a mask and replacement it at depth and without significant disturbance of buoyancy doing so. Having had an incident myself over a flooded mask, and having seen a very competent buddy lose his composure completely over one, I realized just how important this skill is. Those of us who dive in very cold water don't LIKE to take our masks off or flood them, which is precisely why we should.
Human error can include poor gas planning, buddy separation, and diving in conditions you shouldn't. Every dive should have some kind of plan for how much gas the divers have and how it compares to the depth proposed AND the type of dive -- Do we need to get back to an anchor line, or the shore, or can we surface wherever we want? How much gas you hold in reserve varies by the constraints of the dive, but you should always have enough to get you and your buddy to the surface in the event that one of you has a gas emergency.
Practicing good buoyancy control is key to safe diving. Being able to control your position and direction in the water allows, for example, descents where you stay in good buddy contact. Since descent and ascent, when things are changing, are times when issues are likely to arise, these are times when it's most important not to lose touch with one another. Good buoyancy control also minimizes the risk of any kind of decompression illness, whether it's the bends or lung overexpansion injury.
It's also good to work on maximizing your situational awareness. It's very easy to get tunnel vision underwater, whether it's because you're fidding with some equipment issue, or because you're fascinated with something you've found, or you're taking pictures. In the visibility we enjoy in the northern Pacific, you can lose your buddy in just a few seconds if you aren't paying attention. Developing a pattern of checking on your buddy several times a minute will reduce the chances of this, as will developing a good communications system -- If you signal your buddy that you're going to stop and take pictures, it's far less likely he'll swim blithely on while you do so, and be lost in the murk!
Good judgment about where and when and with whom to dive is also very important. I'm assuming that where you are is a lot like where we dive, where conditions can be variable, and some sites are very tricky if you try them at the wrong time. In addition, one has to learn to be honest about one's own capacities. One of the hardest things I've done in diving so far was to call a dive off a chartered boat for which we had paid a good deal of money. The surface conditions were beyond what I felt comfortable with for trying to get back on the boat. But if I didn't dive, most likely my whole team wouldn't, and a lot of money would have been wasted. It was a hard place to be in, but these kinds of situations come up, and people get in trouble when they allow peer pressure or financial considerations to push them into diving where or when they don't think they should.
And that brings up the last thing I want to say about Pacific Northwest diving -- Study what you can learn about the sites you dive. Tides and currents can be fierce up here, and I know jeckyll has written about getting caught in strong current and having a very unpleasant experience.
So, do what you've been doing -- Conservative dives building skill and confidence. Practice emergency procedures, including mask skills, so that you're comfortable with them. Hone your buoyancy, and pay attention to your situational awareness. Develop good underwater communications, and exercise good judgment. Then you won't have to think much about potential problems, because you will have avoided the vast majority of them!