I agree with most of these guys (except Groho. No offense, but caster is usually what causes pull. With the erratic pull conditions you're experiencing, it sounds like something's worn. A worn idler arm bushing is very common and will cause these symptoms. Strut rods are almost as common and can cause a pull as well, but usually the change will come when braking or when going over bumps.

A good alignment shop will check EVERYTHING before aligning the car. It makes no sense to align a vehicle if there are loose parts.