The problem here is the mixup and the misunderstanding between PPI and DPI. In ps you have ppi - pixels per inch. On a printer you have dpi - dots per inch. Two different animals. If you got enough ppi in your image you can print a bigger (dpi) image than if you don't. From ps you can print any size the same as a pod (print on demand) does. An image is available for sale on a pod at several different sizes. The dpi is set with the printer - usually between 150 and 300 depending on the quality of the printer. In ps if you tell it to print an image at say 60 inches, it'll try to do it. But to get a quality print you need at least 6,000 pixels on a side to do it without problems. If the image doesn't have that many pixels to start with you simply can't go that big without posterization. In ps setting the ppi ONLY affects the output digital file. If it's going to a pod, then you usually want 300 ppi, and whatever size fits. For the web you want 72 ppi. Now if the size you want of the image and number of pixels don't match, that's when you have to resample and change either ppi or image size, or both, and within reason it works OK. Without resampling, if you change the image size, the pixels change and vice versa. So, if your trying to sell on a pod (or print yourself) a print that is 16 x 20, then you need at least 6000 pixels on the long side at 300 ppi. If the original image didn't have that many pixels and you try to increase ppi by resampling, ps makes up pixels to fill in the holes. That's where the posterization and odd colors come from.
