This post will cover two window problems.
1) Windows retaining greasy appearance.
2) Windows with paint splatter from paint sprayers.
I have 3 main reasons why I do not use traditional window cleaning products routinely found in stores. They're full of harmful chemicals, they cost too much, and they never do a good job cleaning up greasy messes. I feel no matter what type of clothe I use or which cleaner I use grease on the window appears to smear around the window.
Solution, wet your preferred towel (clothe or paper) and add a dab of dish soap, and get your towel nice and soapy. Wipe your window down. While the window is still wet, dry the window with a dry towel. And that's all there is too it! If you feel you have a NASTY mess, before you dry the window go ahead and go back over the window with just a water soaked towel.
Paint Splatter stuck on window
This is a really easy fix. Make a baking soda paste out of water and baking soda. Use a clothe to scrub the window with the baking soda paste. Clean the window with water and repeat if you missed any spots. The really nice part is most paint sprayer splatter is on the outside of your house, just grab the hose! No need to be dainty when you clean the baking soda paste off.