Well, I've had my M1A for a few months now, and gotten some good range time with it.  It was made 2 years ago and is a standard model. In general, best gun I've ever owned.  There's only one problem that's really eating me up.

The first time I took it out I had some problems with maintaining a zero  I realized that it was because the screw on either the elevation or windage knob wasn't tight enough.  The problem is this- if I tighten both screws so that they are merely snug, its so tight that I can't adjust either the elevation or the windage.  I loosened the elevation knob screw a little bit, and the knobs are tight enough that it holds a zero, and I can still adjust both elevation or windage.  But now I'm not sure how secure that elevation knob screw is.  Any tighter and its so rock solid I can't even turn the knobs.

I realize this is probably an incredibly newbie question...or possibly there's some issue with my rifle.  The manual doesn't address this issue at all, and I haven't heard of any one else having this problem.  I've spent a hell of a lot of time trying to find the combination of the elevation and windage knob being the right tightness where I can still adjust the sights, and they are still solid, and this is the best I could come up with.

The screw on the elevation knob should be tight and left alone. Tension is adjusted with the windage knob nut.

You could have a couple of problems, worn recvr elevation detents , elevation knob sring washer thing is bad or the elevation knob nub is worn.

Alot of the older SA inc rifles had poorly machined recvr detents and SA just used M1 lock bar type sights to fix the problem which could be an option in your case . My guess is you have a bad elev knob...

tension control is the inner screw on the windage knob. I had a bad sight base that would not allow proper tension due to it being machined crooked.

Here's how to adjust and tension the M1/M1A rear sight.

First sight in at 100 yards.
Once you're on target, lower the rear sight all the way down, COUNTING THE CLICKS.
At 100 yards, that number of clicks UP is your zero.  (Usually from 9 to 12 clicks on most rifles).

Once you know your zero, raise the sight that number of clicks.
Pad a pair of pliers with leather to protect the knurling on the elevation knob.
Grab the elevation knob with the WELL padded pliers and hold the knob STILL while you unscrew the elevation knob screw a turn or so.

Being careful to not allow the sight to move, rotate the elevation knob so the 100 yard mark is aligned with the witness mark on the sight drum.
Hold the knob firmly with the pliers so it can't move, and tighten the windage knob screw TIGHT.

Lower the sight, then raise it the number of clicks your 100 yard setting is.
(In other words, if your 100 yard zero is 10 clicks up, when you raise the sight 10 clicks, the 100 yard mark should be aligned with the mark on the drum).
Check the clicks to be sure there's no "1/2" or partial click at the bottom.  If there is, readjust the sight until there are no partial clicks.

To tension the sight, tighten the windage drum's slotted nut until you can't turn the windage knob.
Back off the nut one "click" at a time until you can turn the knob without too much force being needed.

Raise the elevation ALL THE WAY, then push down firmly, but not TOO hard on the sight.
The sight should not drop.  
If it does, the sight needs to be re-tensioned, OR the sight is worn or defective.

If this process doesn't allow you to move BOTH the elevation and windage knobs, the sight may be defective, or mis-installed.

In any case, the elevation screw MUST be TIGHT, the windage screw should be just loose enough that you can rotate it with without undue force.

If you adjust it as above, and things don't work "right", see a gunsmith or return it to the maker.

Quoted: The screw on the elevation knob should be tight and left alone. Tension is adjusted with the windage knob nut. You could have a couple of problems, worn recvr elevation detents , elevation knob sring washer thing is bad or the elevation knob nub is worn. Alot of the older SA inc rifles had poorly machined recvr detents and SA just used M1 lock bar type sights to fix the problem which could be an option in your case . My guess is you have a bad elev knob...

Nothing should be worn on this thing.  I've taken some of the advice here and given it a whirl again tonight.  Nothing.  Its either so tight it won't budge, or so loose that I can move it with my finger. The weird thing is, I got a reasonable fit before by loosening the elevation screw...but that's not the way it should be.

Ok, problem solved.  It turns out the screw on the elevation knob was a little too tight.  Its tight now...but not too tight.  I can turn everything so that it makes nice snaps when I turn it, and the elevation knob passes the finger pressure test.

I've got some pretty good blisters to show for it, but everything is good now.  Thanks to everyone who responded.  Now I understand a little these sights a little better.

For someone who's used to shooting an AR-15, what differences (aside from the obvious cosmetic differences) are there in manipulating the rear sight aperture that might not be immediately apparent to an M1A newbie?

screw on the elevation knob is supposed to be tight. If it is loose, the knob turns but the apeture wont move. M1A sight is 1 click = 1 moa. ARs are 1/2 moa per click.