Welcome to BimmerPost, fellow Bostonian.
Certainly not normal. Considering you've had the alignment checked, I think you would see a huge improvement in just about everything with some new quality tires. Ride quality, noise, and handing would very likely all improve with a tire upgrade at all four corners. While you're getting the new tires mounted and balanced, have them notify you of any bent rims (just in case).
You have tons of choices at that size for tires. My advice would be to read around some E46-specific forums and TireRack reviews to find something that will work for you. Original equipment on your car was the Michelin Energy MXV4 (all season). Make sure you choose a tire that will suit your location. Being from MA, I'm assuming you'll want all seasons (unless you already have a dedicated set of snows, then you could go more performance if you want).
And as others have said, this forum is geared towards the E9x cars (MY 2006+).