I was watching a show were a couple of guys were working on an older vette. There was some slop in the steering. What they did was slightly tighten up a set screw on the steering box, which removed a bunch of play.

I just replaced the front-end on my car, and now that everything is tight, I saw a little bit of play from the shaft that comes out of the box (steering knuckle?) . Can I adjust this out?

Guys who rebuild these boxes for a living strongly recommend against trying to adjust out any slop. Of course they might be motivated by instead recommending you have the box rebuilt, but before I heard this I tried to adjust out the slop on my resto car and it worked for about 10 minutes, then the steering was more sloppy than ever. If the box is really sloppy, do it right and have it rebuilt by someone who knows these boxes and does it right. Just replacing the ball bearings and packing in new grease rarely cures the slop.

Not really sloppy, I noticed that the splined shaft that exits the box (pitman arm/shaft) moves back and forth a little.

I think I answered my own question - the adjustment is for the worm gear right?

The service manual has a procedure for doing this. First, the large diameter end plug is adjusted to a specified torque on the steering shaft and then the lash adjustment screw is turned to take out all lask and then the locknut is tightened.

The set screw should be for adjusting the pitman shaft on the ball nut. Worm bearing preload I think is adjusted thru where the coupler goes on, and the cap opposite, when the box is assembled.

The set screw should adjust shaft up and down movement as well as some back/forth, both of which translate into steering wheel play.

Grab the steering coupler and rotate it back and forth thru center as you watch the pitman shaft. If it seems to have excessive movement at the coupler before the splined shaft begins to turn, there may be room for adjustment.

If you get it too tight, it will quickly become loose, begin to stick, or break internal parts, causing steering loss.

There are service manual instructions which involve removing the pitman arm and the steering wheel, and checking the amount of torque needed to turn the shaft with an inch lb torque wrench at the steering column.

Definitely read through the whole service manual instructions for on car adjustments before attempting. I'm just going by what memory I think I have.

I believe they actually refer to the parts in the gearbox as the rack and the pinion...

But in any case the 3 gear teeth on the pitman shaft are tapered. The set screw on top adjusts the tolerance between the pitman shaft gear (or pinion) and the rack gear. The problem with this adjustment is that the majority of wear is in the on center position, so adjusting that to be tight can result in excessive tension for off center (turning) operation.