I currently use a Nikon DX200, admittedly an old camera. With that camera, if I want to check image quality, I use the magnify function and the thumb wheel. This allows me to zoom in on the image to a small area and see if it is in sharp focus. The process is a bit tedious.
Are there faster strategies for determining whether the image is in focus on this kind of camera? What new features do modern cameras have to make this action easier?
Do you mean a Nikon D200 (which is a DX camera)?
A key question is whether you shoot raw. If you do, there is a trick you can use, and that is to set sharpening in the camera up to the maximum (see the Shooting Menu, Optimize Image).
This will affect JPG images and the preview image, but will not affect the raw image (see note below). By doing this, you get a way-too-sharpened image to preview, which will look visibly more "crisp" (for want of a better word) when you are both in focus and without motion blur. This works especially well on subjects where there is a lot of texture, e.g. grass, leaves, and is a good way to tell the area where your depth of field is centered.
This is NOT a good idea at all if you are using the JPG's out of the camera, as they will have way too much sharpening applied.
Note also if you use Nikon's software to "develop" your RAW images, they will default to the in-camera setting, and will come out too sharp; those can be reset however. But if you use Nikon software this is not a very good approach as you will have to turn off the setting on each shot.
For Adobe and (as best I know) any other raw conversion software, the setting is ignored, and has no effect on the resulting image, which is why it can be handy as an in-camera-only viewing aid.
This is not a substitute for zooming in, but I find I do not need to zoom in as far, or look as closely, as otherwise.