If the steering effort feels heavy, this can be caused by a power steering fluid leak. Some models may have burrs on the return port of the power steering reservoir that create a gap between the hose and the port. Sanding the burrs off the port and replacing the power steering return hose is the repair for this concern.
Car problem reports
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Newest reported 2010 Mazda Mazda3 problems
The rear brakes can squeak because the rear brake pad may be contacting the brake rotor. A burr on the backing plate of the brake pad can prevent the pad from seating in the bracket properly causing the contact with the rotor. The backing plate and the pad support hardware can be deburred in the contact areas. Mazda has also released revised brake pads.
A vibration felt at 55 mph may not be a tire problem. Mazda has revised motor mounts available which may help remedy this problem.
The engine may be difficult to start in extremely cold weather (-20F) after a short trip. This can be caused by sticking main relay points.