Are focus and noise problems I see with my Nikon D80 simply because newer cameras are better?
No. We're talking about a camera that's 10 years old, so you can certainly expect better performance from a newer model, but the D80 is capable of focusing just fine and noise shouldn't be a problem if you're shooting at a reasonably low ISO.
Compare your results to the [sample images at DPReview]. If your images are worse with respect to either focus or noise you may be doing something wrong or need to adjust your camera or have it serviced.
I can't seem to get photos with good focus or without noise.
Those are two distinct issues, so lets take them one at a time:
focus: Your camera should be able to achieve sharp focus on something, even if it's not the thing that you intend. Test this by using a focusing target like the ones from DSLRKIT, or just take a photo where there are a number of objects at gradually increasing distances. For example, you could take a photo of a picket fence at an angle, so that each picket is a little farther away.
Shoot your test shots with the lens at it's widest aperture and also at a medium aperture like f/8. The wide aperture shots will make it easier to see where the best focus is, since you'll have the smallest depth of field, but lenses typically perform best around f/8, so you'll get the sharpest image at that setting. Also, be sure to keep the exposure short -- maybe 1/500s or 1/1000s to eliminate any chance of motion blur.
If there's no area of sharp focus, then there's a problem. Try again with a different lens to eliminate the lens as the source of the problem. If there is an area of sharp focus but it's not where you expected it to be, then you need to adjust the camera for front or back focus.
noise: Sensors have improved over the past decade, so noise will be a bigger problem on the D80 than on something much newer, but you should still be able to get a pretty clean image if you're taking shots with plenty of light at a low ISO setting. Posting a few examples of images that you're concerned about, including the camera settings for each shot, will help people here give you a better idea of whether there's a real problem. Try shooting outdoors in full daylight at low ISO -- 100 or 200.