I've noticed that when my '88 420SEL looses traction in the wet (or dry for that matter) only the right wheel spins, the left one sticks to the pavement as far as I can tell. Should this car have any kind of positraction, or something to keep one wheel from just spinning, and spinning, and spinning?

I've actually had problems getting up hills because I can't get enough traction on wet asphalt. I've almost had an accident or two just from not being able to turn out into traffic fast enough.

I don't think this would be a problem if the previous owner hadn't put such cheap tires on the car (Coopers).
If this is normal for the car, would better tires make that much of a difference? I am going to replace the tires, regardless, in a month or so when I have enough $$ for new rims.