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.
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Newest reported 2009 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.
If you hear a constant grinding noise from the front brakes, even when not pressing the brake pedal, it is possible the wheel hub has shifted in the steering knuckle causing the brake rotor to grind against the caliper bracket. The hub will need to be inspected (replaced if necessary) and Mazda has a repair procedure for this concern.
A vibration felt at 55 mph may not be a tire problem. Mazda has revised motor mounts available which may help remedy this problem.