I have a 1989 420SEL and the left rear window is inop. The motor works but the arm inside the door doesn't seem to be engaging the window. What is the best way to fix it?

Take off the door panel and examine whats broke. I think you can purchase a new window regulator.
I'm not sure about you model but with most models this type of repair is well within the scope of the backyard mechanic.

__________________
1990 190E 2.6
1996 Grand Voyager 3.3
1985 Mustang GT 5.0 5 SPD
1982 Suzuki GS 750T

What usually breaks is the plastic slider or sliding jaw. I've never done a front one, but I imagine it's similar to the rear. If you do it yourself, be aware that the regulator has a spring that's willing and able to pinch fingers. Also be careful that you support the opposite end of the pin when peening it. You can break the new slider if you support only the plastic. There might be something in the archives about what lube to use.

Sixto
91 300SE
81 300SD