2001 Mercury Mountaineer pulsating brakes

First remove that wheel and check for debris that cracked off the wheel and got wedged between it and the rotor, especially if you have cast wheels. Next, remove the caliper and rotor and look at the backside of the rotor where it contacts the hub. You'll find one or three little raised spots of rust corresponding to the access holes in the hub. When those spots aren't cleaned off and the rotor is reinstalled in a different orientation than it was, those raised spots prevent the rotor from sitting squarely on the hub. It wobbles and that makes the caliper slide back and forth. That tugs on the steering linkage so you may feel the wobble in the steering wheel or the brake pedal.

Also be aware that on Ford trucks, the front rotors fit uncommonly tightly on the hub. If yours are original, you fought really hard to get that one off. The same thing can happen when putting it back on. Eventually the wheel will push it on, but then the lug nuts will be loose. That will grind on the wheel and lug nuts and destroy the machined friction surface that holds the nuts tight. The only fix for that is a new wheel and new lug nuts. You can use anti-seize compound on the hub where the rotor sits, but be absolutely certain no grease of any kind gets on the wheel where the lug nuts make contact.

Be sure to use a torque wrench on the lug nuts. Failure to torque the nuts properly is the only cause of damaged threads and stripped lug nuts, but that won't show up until the next time someone tries to remove them. Over-tightening the nuts leads to them breaking.