I've fitted a bunch of barrels, you need to make sure there's minimal gap at the frame, initially, the easiest way to see that is to hold it up to a bright light and look across at the level of the firing pin and above it, usually there will be a slight gap at the top, narrowing towards the bottom. If there's no visible gap and the barrel isn't loose when it's locked up with no forend on it, check the gap with feeler gauge blades to see what kind of gap is actually there, a well fitted factory barrel will be tight on a .001" blade, but not all are that tight, a lot with be snug on .001" and tight on .002". You can check it at the very top and on each side, sometimes they'll be tighter on one side than the other too. Once that gap is as it should be and the barrel locks up tight with absolutely no movement
without the forend on, then work on the latch engagement, .080" max, .060" is pretty much ideal and works very well for me. As Larry said, the closer you get to the max, the sooner the latch will reach its maximum travel as the shelf wears and the barrel will be loose.
Another issue that you'll see is the barrel face won't be flat, so you'll see a gap on just part of the area where the barrel meets the standing breech, this also more than likely means there's too much headspace and should be checked and corrected before fitting the barrel, I explain that in the barrel fitting instructions.
Tim