Nikon D60 Photo Quality?

I have a Nikon D60. When I set my camera to Auto, the pictures are very good quality. When I set the dial to the "P" (Programmed Auto) or say "A" (Aperture-Priority Auto) the quality is considerably worse. Its grainy and just doesn't look very nice. Could this be a problem with the camera itself, the lens, or just me as a photographer?

You need to learn to use your camera properly. My D200 normally stays on Program.

I think you need a new eye glasses. My friend.

The D60 won't do well at high ISO, so I'd avoid shooting with auto ISO setting above 400.

The mode setting should have no effect on your image quality if it's properly exposing your pictures. I suspect there's some difference in other aspects of the photos you're comparing. If they're underexposed and you need to adjust the exposure in post-processing, you're going to get color noise. If your subject has lots of continuous tones, you're going to see color noise if you look. You're going to see color noise in shadows even in well-exposed daylight shots with this camera if you're looking at it pixel by pixel, and indoors in dimmer lighting it's going to be noisy in many situations, particularly if you're upping the ISO to get faster shutter speeds.

It can take great pictures within its limitations, but it needs good light on that old sensor.

You as a photographer because you don't know how the settings work.

P and A mode are modes that give you more control over your settings; A mode more so than P. This means that the camera does not attempt to change settings on its own according to the conditions- you determine everything yourself. In auto mode, you may notice that under low-light situations, the camera will use the flash at a low ISO setting which is what it thinks is the "best".It will give you results something like this:

In P, A, S, or M mode, the flash never activates unless you tell you to, and you have the option of controlling your ISO setting. The reason why photos are coming out grainy is because you either selected "AUTO ISO" for your ISO setting, or you set it really high, say over ISO 800. If you want grain-free picture with lighting that'll look natural, set your camera to A mode, select ISO 100, and put it on a tripod.

Actually it's a problem with you. Apparently you haven't done your home work sport. You need to learn how to operate a dslr camera - not just pick it up and expect shots like the professionals do…
it doesn't work that way.

Home work - read, practice, perhaps a short course at a local school. Anything you can do to learn your camera.

Right now what you've got is an expensive paper weight. When you learn how to use it then you'll have a camera.