If the speedo is working, transmission shifts normal, and the ABS lamp is off, the rear speed sensor is fine.
If the ABS lamp is off and the brakes have a skipping feeling when slowing from 8 to 3mph, then corrosion has lifted one or both front wheel speed sensors out of place (or a front wheel bearing is worn out). If the front sensors were bad, the ABS lamp would be illuminated (broken wire or broken sensor).
As for the tire size change, again an ABS lamp would be illuminated and a fault code stored. And the lamp wouldn't illuminate at startup, but rather after reaching 20 mph or so.
With the front wheels off the ground, key off, grab the top and bottom of each tire and rock in and out. Movement=bad wheel bearing assy (which will also give the brakes a skipping feeling, again while slowing between 8 and 3mph). No movement= proceed to unplug each wheel speed sensor and connect a multimeter set on ACmv. Hand spin each wheel. Each side will generate a small AC voltage. Whichever side is least consistent will be the problem side.
Remove the caliper ear assy and rotor on that side, and remove the allen screw for that sensor. Then proceed to read this
http://www.carquest.com/common/downloads/partsTechBrakeCQB 02-02.pdf
If the sensor does not pull out easily, it has a growth of corrosion grabbing the O-ring. The only solution in this case is to replace the sensor (once forcibly removed) with a new one.
And lastly, find a new mechanic, or at least teach him how to use a Tech II. And do all the burnouts you feel like doing, BECAUSE your problem is unrelated.