My mother-in-law has a 2003 Buick and the air blows out cold on one side and hot on the other. I've had to add freon once each summer for a few years now, but this has never happened. It doesn't have separate controls like my Bonneville. She thinks it must need more freon, but I don't think that's her only problem.
Any ideas?

Since you say it's not a dual control system, the problem is most likely the freon level. The passenger side gets the incoming freon first. If there's not enough pressurized freon, that evaporates on the passenger side cooling air there in the coils; then the side of the coils where the driver's air goes through doesn't have enough freon to cool them.

If the passenger side is colder than the driver side, then you're low on freon. Perhaps previous summers not enough has been added to compensate for the amount lost over the years.

You might check for signs of oil around the schrader valves for putting freon in and see if the valve is seeping freon, which usually leaves an oily residue around the exit point.

Otherwise, you might want to have the system leak checked and fully charged.