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 my car have any kind of positraction, or something to keep one wheel from 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.