The "best" resolution you can get out of a printed photograph (4" x 6") is about 300 dots per inch (dpi). There isn't any more resolution in that print.
When you scan, the image is a particular dpi, and most programs will tend to fit to screen as there is not physical width and height to the image you scanned. It is just a bunch of pixels. If you scan at 1200 dpi, there will be many "duplicated" pixels adjacent to one another as you can't force more resolution out of that picture.
If you scanned at a high resolution (thinking you would get a better image), and tried to display it on the screen, it would get blown up and you'd see the difference between the physical resolution of the print and the desired resolution that you scanned it at.
This website has a lot of great information on scanning: http://www.scantips.com
Scanner. Your scanner is producting an image in a specific format and resolution. Your computer only reads that, and has no way of controling it, or improving it.
Try to see if you can locate the scanner "settings", and adjust this for the best posible format.