I have a 2001 F250 4 wheel drive. I've been reading here a lot about wandering issues and thought I would share my experiences and what helped. Seems like this is a very common issue!
My truck drove fine at 230,000 miles with bad ball joints and mismatched tires....replaced tires and still drove great! Got ball joints replaced and that is where my wandering journey began. Got a front end alignment and still wandered. Took it for a second alignment to a shop that was highly recommended...they said it was the new stabilizer causing the problem. Replaced stabilizer and still wandered. Drove truck from Tennessee to Florida and was a real white knuckle experience! Took it to a third alignment shop and they showed me that everything was dead on and didn't need alignment. Adjusted steering box...still wandered!!! Paid approximately $80 for a Bilstiene stabilizer and it still wandered! I'm pulling my hair out about this point. Took it to a Ford master mechanic who said it was the steering gear box and he would replace for $550.00 - ouch! Told him I didn't think that was the problem since it started immediately after ball joints. So I didn't replace the steering gear.
Which brings me up to today. I decided to adjust the toe myself with a tape measure. With the help of this forum I determined that the best toe in would be 1/8 inch. Initial measurements before adjusting was 1/16 inch. I adjusted each tie rod approximately 1/2 turn and HAPPY DAYS!!!! My truck drove much better. Not perfect yet but much, much better. No more constant correcting the steering. The measurement at this point is approximately 3/16 toe in. I'm gonna keep a close eye on the tires for wear...but at this point I don't care if I have to rotate them frequently as long as I don't have to fight the steering anymore.
Anyway thank you for all the great posts on this forum. And I hope this helps someone else out there that is fighting the same problem. It was discouraging at times and took almost 8 months to finally get to this point. I won't go into detail here about how to adjust the toe as there are already many post on that subject that can be searched for. Good luck!

 

Seems like a lot of toe, I run 1/32" and it tracks straight, no wandering. I would bet whoever changed the ball joints moved the caster bushings and didn't set it back where it was. Find a good alignment shop and have them put as much positive caster in as the bushings will allow.

 

I did the same thing a while ago and my front tires are starting to wear funny on the outsides. As soon as I can I am going to get it realigned and like others have said I am going to have them max out the caster..