Yes, you can tell what went wrong:
- out of focus (entire frame)
This can be a problem because of close-focus, i.e., the lens and camera never did find something to lock onto before you fired and was focusing ahead of everything in the scene. Sometimes this is because your lens focuses too slow, sometimes it's because there wasn't enough light to provide enough contrast to allow the camera to lock-on so it did it's seek-cycle, trying to find something, then gave up, AND then you fired. You'll KNOW if you did this, and will cuss yourself, but we all do it. Once.
For a close subject, it might be too close and the lens can't focus close enough. Move back, or tell the subject to step closer to the canyon behind them. It could be the result of your lens being set to not allow it's closest focusing range because it slows the seek. Canon's 70-200L f2.8 has a switch to control that, and it occasionally caug... strike that. I never had that problem.
It can even be the result of a damaged body or lens mount, making the image never focus on the sensor/film correctly - I've been there and done that and it was really annoying to diagnose, then get fixed, and, with a pro-body and lens, can be very expensive. Uh. Yeah. I did that running to get away from a bull while shooting pro-rodeo and flipped over the fence. Broke my Nikon D1x and 70-200f 2.8 at the same time but the bull didn't get me.
- depth of field (focus on wrong element)
This is easier to diagnose. Something in the image is in focus, but it's not what you wanted. Sometimes it's the result of having a different sensor chosen than you thought. My favorite stunt.
It can happen because you need continuous focus because your subject is moving toward or away from you, and the camera locked focus, instead of following the subject. This is a problem that bites all sports-action photographers periodically, usually after they have been shooting something else, or loaned their camera to their wife or girlfriend, who messed with the settings. And, no, I have NEVER experienced THAT. :-)
- motion blur (not fast enough shutter speed)
Usually this shows up as the main subject is a streak in the scene, but could be that their extremities are blurred if they were moving hands, feet or maybe their head. The torso moves less than the other parts and usually is not (as) blurry.
An alternate, but much more desirable result, is when you are panning with the subject, fire, realize the shutter is taking too long, but you keep panning. Your background will blur but the subject will still look good. I used this a lot for my sports photography - doing it deliberately, not like Peewee Herman, where "I meant to do that."
- camera shake (hand-held, shutter too slow)
This occurs most when you're using a long-lens in lower-light. Generally the motion blur is equally squiggly all over the frame. If the problem occurs with a still-life or landscape and you have IS, you might be able to fix it by turning that on, unless it was already on. A tripod could help. Set up some big strobes and light the heck out of it. Increase your ISO, open the aperture more... do something to increase the available light hitting the sensor.
EDIT: Regarding learning how to pan
Panning is really easy, it just takes some practice and knowing a trick.
Here's a good way to practice: Set your camera to its shutter-priority mode (whatever it's called in your camera) and set 1/60 as your exposure time. Using a long-ish lens, in the 200mm range, stand a little ways from a busy road, maybe 50 feet, and as cars pass try to get a photo of a wheel or the door handle.
The trick to panning correctly is to sync to the speed of your subject quickly, so face the roadway, then pivot at your waist/hips to view the approaching vehicle. As soon as you see it, start tracking its motion, then, as it nears being right in front of you, fire and continue panning. You should see your target in the view finder before you fire, and it should still be there when the shutter opens again. If so, you were panning at the right speed for the subject and you should have little to no motion blur of the target. If the target wasn't in the same place as it was when the shutter released then you didn't pan smoothly.
It's important to stand in a balanced position, at least until you've been doing it a while and it's all second nature. Similar to shooting a rifle, you want your feet about as far apart as your shoulders. Face the road where you intend to release the shutter, not where you'll see the car first. You need to pivot smoothly from the hips as you learn, because swinging your arms or rotating your upper-body will make the camera rotate, leading to photos with verticals that are not vertical, leading to post-processing, which is no fun.
And, again, the goal is to have the target, whatever you're shooting, be in the viewfinder before and after the shutter opens and closes.