My Nikon D300 has quite a few autofocus points. There's a button I can operate with my thumb to change the autofocus point but I find that quite difficult to use. So I almost exclusively use the center point to focus and then hold and compose the picture.
Are there any advantages to use any of the other autofocus points (Am I missing out on something)?
A number of articles have been written about the problem with the focus and recompose technique. While the general idea they espouse is theoretically correct, most of them are really actually wrong on a number of points. First and foremost, most of them assume that you want to focus at the extreme corner of your picture. While you can do that, it's pretty unusual. Second, they assume that you'd be able to select a focus point there when you did want it -- but I don't know of any camera that has focus points at the extreme corners.
If we start with a more realistic assumption of focusing at, say a "rule" of thirds line, the focus shift from re-composing is reduced dramatically. For example, with a 50mm lens on a full-frame camera, the focus shift is reduced from 12 cm to about 1.5 cm. In a typical case of shooting hand-held while standing up, 1.5 cm is completely inconsequential -- most people can't stand still enough to maintain distance that accurately in any case.
Even if (for example) you were shooting from a tripod so you maintained the camera position perfectly, and really did want to focus at the extreme corner, I doubt the focus shift from re-composing would mean much anyway. Your best chance of seeing focus shift would be when focusing at the extreme corner with a fast, wide-angle lens. It's almost certainly true that if you focus and re-compose, that extreme corner won't be tack-sharp. If, for example, you computed the exact focus shift and moved your camera/tripod to compensate, you probably wouldn't be able to see any real difference (and if you did, it might just about as easily be less sharp instead of more). Why? For the simple reason that there's virtually no such thing as a fast, wide-angle lens that can produce extremely high resolution at the corners at maximum aperture. It's going to look pretty blurry, regardless of precise focus.
As to the possibility of it looking worse: the simple fact is that most fast, wide-angle lenses show at least some curvature of field. Depending on the exact amount, maintaining exactly the same distance from camera to subject may easily (in fact, often will) actually move you further from perfect focus at the corner than if you focus and re-compose. If you do want to do this, however, it's generally pretty harmless -- as discussed above, the resolution at the corners is usually low enough to hide small focusing errors in any case.
In most higher-end cameras (almost certainly including the D300) the center focus sensor is an f/2.8 sensor. The sensors closest to the edges of the frame are usually f/5.6 or f/6.3 (or so) sensors. The faster sensors are inherently more accurate than the slower ones. This means that even though a sensor close to the edge of the frame may be measuring (something closer to) the correct distance, it may well do it enough less accurately that the focus distance ends up less accurate overall.
Some people point to macro shooting as a possible case where re-composing would be a problem. They do have something of a point -- in macro, DoF becomes so thin that focus errors that would normally be inconsequential become quite important. On the other hand, at least as a rule, macro work involves manual focus anyway.
Summary: The advice against focusing and re-composing is largely based on false, unsupportable assumptions. In real shooting, it's nearly impossible to find a situation where the theoretical problems become even marginally relevant.
There are two main cases:
Focus and recompose can cause misofocus when using really fast lenses as by rotating the camera the focal plane rotates and thus will no longer pass exactly through your subject. Most of the time the subject will still be within the depth of field so this effect goes unnoticed, however with shallow depth of field focus and recompose may fail. In this situation using the outer points allow you to focus an off-centre composition without having to recompose.
Timing shots can be difficult with focus and recompose. The time taken to move the camera to change composition and settle the motion can be too high in some cases when you are waiting for some sort of action. Here it is better to use an off-centre point when necessary so you can keep the camera still and just fire the shutter when needed.
In addition, tracking a subject with unpredictable motion - you might want to enable to camera to use as many focus points as possible and automatically switch focus point as the subject moves across the frame.
I'm also using center point all the time.
But when I'm shooting sport, I use also other points. When I want to preserve golden ratio or compose scene in movement (with focus on moving object).
Most of the time I use the centre point, when I need focus off-centre I mostly use focus lock and re-frame.
However, when I'm shooting a still life of an assemblage of objects, I usually get the composition right with the camera locked in position on a tripod. I then often take a series of shots playing about with aperture etc. I find it more convenient to select an off-centre focus point than to keep unlocking the tripod head, focusing and then reframing - and this would make it hard to keep exact framing in successive shots.
The other time I use an off-centre focus point is (as others have said) when I want to wait for and capture the "right" moment with a moving subject of any sort, with an off-centre composition. I'm not fast enough to recognise the instant, move, refocus, recompose and shoot.
