for the photo printing.. do you use a photo editing program?
There are some nice free ones that can sharpen, lighten, crop, auto adjust..
Google's Picasa is nice I've used it for years.
http://picasa.google.com/
You could try making adjustments on a photo and then see if the printer does a better with it.
My Epson has in the main tab of the printing preferences a Mode section for photo enhance, custom, automatic...
Is there something like that for your HP?