A good alignment tech should inspect the suspension for worn parts before performing an alignment. There are a number of things that could cause a wander; other than the alignment being off.
Ball joints
Tie rod end
Control arm bushings
Control arm shaft bushings (different thing than the above)
Loose wheel bearing
Worn or out of adjustment steering gear box
Worn idler arm
Drag link (sometimes called a center link)
In the rear one should inspect for loose wheel bearings, worn trailing arm bushings, etc. but odds are the problem is up front.