When I finish a load of laundry there is lint on all the clothes.

Could be a back up in the washer drain filter, check that, but any lint would be removed in the dryer with the aid of a softener sheet.

Do you have one of the newer front loaders?
They have two things that many people don't notice (because they don't read the manual):
1. A drain hole in the rubber gasket around the opening, that clogs with lint. Simply remove the clog.
2. A drain hose in a small door at the bottom front, that needs to be opened into a flat pan (like a brownie pan) once in a while. You may have to check the manual. Look for a copy online if you lost yours.