If you clean the inside first, you'll know the smears are outside. You'll be able to tell which side has streaks. Newspapers are good for a lot of things, but not for drying windows. Newsprint isn't very absorbent, and some can smudge your hands and sills. For lightly soiled windows, mix 4 tablespoons lemon juice or vinegar in 1 gallon of water.
Vacuum screens regularly from the inside.
Use a light hand so you don't stretch or tear them. To wash them while they hang, put your hand in a cotton glove. Dip the glove in soapy water, then use your fingers on the top and bottom of the blades. Try this Before you clean your house, open the window coverings and turn on the lights. Get as much light as possible.