What's the worst that can happen with over-inflated tires?

Don't go back there, they obviously don't know what they're doing. I used to work at a car dealership and since this is such a simple task this tells me there must've been miscommunication there. Put air in the tires at the recommended rating yourself. Remember just because the tire says it can inflate to (insert some number around 40 to 50+ psi) that doesn't mean you have to inflate it so high. Your car sounds like a sedan, 32psi is okay, start with that and check about once a month. Oh, and remove all heavy objects from the trunk, they just add to the car's overall weight load thus increasing the need to check tire pressure more often.

Not so good things that can happen with over-inflated tires include: 1) tires can lose traction because the shape of the tire actually becomes deformed by excessive air pressure (decreasing the tire’s footprint on the road) causing you to buy new tires faster, 2) tires can be more prone to damage, 3) become stiffer and may not react as expected to common road hazards like potholes, and 4) tires can even give your vehicle a harsh, noisy ride. Hope this helps.