Depends on what is causing the icky look.
One thing that can make clothes look dingy is, ironically, using too much detergent. Try washing a load of clothes with no detergent. Check the machine after it's been running for a few minutes to see if there are any suds in the water. If there are, your detergent isn't getting completely rinsed out.
If that's the case, try washing everything with no detergent a couple of times to see if the look of the clothing improves.