The first "classic" 35mm camera was the rangefinder. It remains popular with many, but the single lens reflex has outsold it for many years. Both types, however, are often perceived as complex, however much automation has been incorporated. They are also relatively large and heavy. Manufacturers are always seeking to expand their market. One result of this search is the compact point and shoot camera. Not only are they small and light, they don't cost a lot.
As with any other tool, there is a place for the point and shoot--and there is also a time to put it away. Let's start with advantages:
Most point and shoots have automatic exposure and focus, which increases the probability of getting a good picture if you're working in a fast-changing situation. They're also small and light, which can keep you free to move around.
The small size and light weight makes it easy to pack one of these cameras and take it more places. I would never leave a camera in the glove box, but if you don't want to put it in your pocket, you could put it in a small lunch-size cooler and have it in the trunk or a compartment. A camera at home or in the office is of no use when you're out somewhere!
Many of these cameras are "weatherproof" or "waterproof." Just what this means varies from one camera to another (and should be checked before buying). As always, safety first, but poor weather has many possibilities for the rail or nature photographer. For the fire photographer, there's often water spraying at fire scenes, not to mention an increase of incidents during bad weather, so real waterproofing can save a large repair bill (if not replacement).
These cameras are designed to be used by people who don't know a lot about them. I long ago learned never to call anything foolproof, for fools are very ingenious, but if you need to have someone else take a photo, you substantially increase your chances of a good result with a simpler camera.
Fill flash is generally very easy to do -- just turn the flash on. No mess, no calculations, although sometimes it can take a lot of button-pushing to do this.
Of course, you don't get off that easily. There are some potential problems with these cameras.
The flash is usually quite limited. You won't be shooting from 50 feet away at night with one of these. They work best for daylight fill and close-ups. Check your instructions for the maximum flash distance and cut back by a third at night.
The flash on a point and shoot camera is not removable or otherwise adjustable (although they can be used to trigger another, more powerful flash unit). Not only does this mean that you can't use cross-lighting to get a good shadow, the location of most of these flashes makes "red-eye" a good probability. Some are even designed in a way that seems to encourage the user to cover them with a finger.
Most of these cameras have little, if any, control over the exposure. They rely on latitude -- the ability of the film or sensor to deliver an acceptable result when not exposed properly. The problem is that this results in burned-out bright areas (highlights) or blocked-up shadows, along with an increase in grain (film) or noise (digital). If you want good prints or enlargements in a variety of conditions, you'll want to be able to do some minimal overrides, such as +2 stops. Most also do not give you any indication of the exposure being used, other than an "idiot light" to warn that it's beyond the camera's capabilities or that you should use flash. For shutter-speed-critical uses such as moving trains, this can cause problems.
The accuracy of the finders on these cameras varies. Until you are sure on this, allow some extra space. Check the instructions to learn how to adjust for close distances. You also need to be sure that you're looking square into the finder or you'll lose heads (or least give someone a haircut).
A few of this kind of camera have fixed focal length lenses with decent speed (such as 28 or 35mm f2.8), but many have zooms that start at f4.5 and end around f12. The longer the zoom, the more this will be the case. This practically requires 400 film as a minimum, or increases the noise level of digital photos. It also limits the flash range at the long-zoom end.
Some are just plain cheap. The price should tell you. A $25 camera isn't going to have a good lens on it if you want to make 8x10's, and it probably won't be very well built, either. On the other hand, a good point and shoot can take a picture that's indistinguishable from an SLR (sometimes even better, because there's no mirror bouncing around). Along these lines, some small digital cameras are 2 megapixels or less. This will limit you to a maximum of 5 x 7 inch prints.
A point and shoot camera can be a good addition to your photo gear, as well as a good all-around camera if you're a more casual user. I've taken one to a lot of places where I would not (or could not) take a larger camera. But, as always, for best results, they require awareness of their limitations -- and with that knowledge, they can make great photos.