How do I make sure my miter joints are perfectly tight?

A tiny gap on one seam ussually means the error is stacking up as you go around the frame. All four miters multiply off each other, so even if each corner tested true on an offcut, a half degree of error on two pieces shows up as a visible gap by the time you close the loop. My fix is to cut all four pieces in one session with a stop block on the same fence setup, and cut them slightly long. Then I sneak up on the fit with a shooting board and a sharp plane, shaving a hair at a time untill a dry clamp closes every seam. Test with the mating piece, not the offcut. The offcut can be true while the actual workpiece drifted a little on the sled or miter gauge.

Been chasing perfect miters since before the fancy glue bottles came around, and here's the thing even a closed seam won't save you. End grain soaks up glue like a sponge and a mitered frame is mostly end grain, so that joint is weak no matter how pretty the fit is. I cut splines across every corner now, either with a slot cutter or just a handsaw and chisel, and glue in some loose keys. My old mentor used hide glue for these because you can rub the joint back apart someday if it ever needs fixing. Do the dry fit over and over till you're sick of it, then glue up with cauls so the clamps press square instead of denting your corners.

Second the shooting board advice, that's the only thing that ever worked for me on wide miters. I label each corner with chalk (1, 2, 3, 4) so I never lose track of which piece mates with which, because once you start shaving them down they stop being interchangeable. Also I dry clamp the whole frame overnight with rubber bands and check it square with a tape measure corner to corner before any glue goes down. If the diagonals match, the glue up goes smooth. If they don't, better to find out with dry wood.

One thing that bit me on wide miters is the pieces skating sideways when you tighten the clamps, becuase end grain on end grain has almost no friction and all that squeezing pressure just slides the joint out of alignment. I run a strip of blue tape down the outside face of each corner now, right across the seam, which acts like a hinge and holds everything in register while the clamps close. Also do the flashlight test before glue up, kill the overhead light and hold a small light behind each seam, because a gap you can't see in daylight shows up instantly as a bright line. If it passes that, it'll close under glue.

Update: got it closed up. The chalk labeling trick saved me, once I stopped treating the pieces as interchangeable and shaved each corner to match its mate, the gaps disappeared. Also tried the blue tape on the outside of the joints and nothing skated when I tightened the clamps this time. Frame is solid, no wobble at all. Thanks everyone.