The most basic check of your mount's polar alignment to the NCP (North Celestial Pole) is pretty infallible.
I had been infrequently polar aligning my mount, primarily because it is pier mounted, and my initial alignment using the Autostar II hand box with a Starlock unit reported good alignment with targets found via High Precision ON almost without fail.
Until my Starlock failed. After concluding the unit could not be repaired and would not be replaced via Meade, I stepped down to manually centering stars during the High Precision routine and shooting my astrophotos without any additional guiding assistance, just the RA motor itself.
But that led me to do a manual drift test to see how well my alignment really was, because without Starlock even if the RA tracking was spot on, any error in alignment would create declination drift. So, I drifted. And lo and behold, I was not pointing at the NCP after all; Starlock was compensating for it just fine and the built-in alignment routines were satisfied with how little I was offset from the true NCP, but I was not pointing at the NCP for the last two years. And so, it was time for a correction to my mount's axes.
Drift Test
A drift test is performed by studying how two stars track in a magnified eyepiece (or live image from your astro camera), one at your meridian (due south) and one at your eastern horizon. If those stars drift either north or south from either of those two positions, the geometry involved dictates which way your mount is pointing in error. It is an unequivocal test, and it gives a reliable corrective action to be taken.
At the Meridian
With your drive running in sidereal mode, you select a star near the meridian, also near the celestial equator. Many of you have software that runs with your mount that makes this quite easy. I use ASIAIR Plus and go to the atlas view to pick a suitable star. We are talking due south at Declination = Zero. Pick a star west of the meridian, though, so that you don't get called for a meridian flip part way into your drift test. Lastly, whether you use a reticle eyepiece or your camera view, make sure your crosshairs are lined up north/south and east/west. Rotate until this is so. This will not be fun or easy if that is not the case.
I center my star in the ASIAIR Plus crosshairs, then go to the Focus mode since it zooms and also runs fast, short exposures. I pinch out to have an easy view of any movement, start a timer, and I watch. Ignore all movements in RA; for a drift test we only need to see if the star deviates north or south from a true east-west line.
If it drifts north, the telescope's mount is pointing too far West.
If it drifts south, the telescope's mount is pointing too far East.
Depending on your mount, the very act of loosening and retightening the azimuth tensioner might slightly change your azimuth setting. So, there is a little bit of back and forth to do here.
If you see drift, a good approach is to loosen the azimuth knob only enough that you can make your east/west tweaks. For each tweak, note which way the star jumps, then use your hand controller to recenter that star, and drift it again. Keep tweaking like this until you've eliminated the north/south drift. A target might be no drift for at least as long as you would want a light exposure sub to run.
The hardest part is tightening the azimuth locking knob without changing your telescope's azimuth at all. As you tighten, you need that star to stay on the east-west line since that is now defining the perfect azimuth. Do only as much tightening that keeps the star on the screen. Whatever way it moves, use small azimuth tweaks to allow the mount to push that star anywhere back on the other side along the east-west crosshair line. Then give another little tightening of the azimuth locking knob which should push the star the rest of the way, if not more, with continued tightening. Keep iterating like that, ensuring that the star's final position is on the east-west crosshair when the locking knob is fully tightened.
At the Eastern Horizon
Now select a star about 20 to 30 degrees above the eastern horizon, again near the celestial equator.
Center that star in the ASIAIR Plus crosshairs, then use the Focus mode for the fast, short exposures. Start a timer, and watch. Ignore all movements in RA; for this drift test we only need to see if the star deviates north or south from a true east-west line.
If it drifts north, the telescope's mount is pointing too high.
If it drifts south, the telescope's mount is pointing too low.
Now again comes the delicate part. Tightening down the altitude knob after you've eliminated the drift will likely be tricky, more so than the azimuth process. Again, loosen the knob only enough that you can make your up/down tweaks. For each tweak, note which way the star jumps, then use your hand controller to recenter that star, and drift it again. Keep tweaking like this until you've eliminated the north/south drift.
Tightening the altitude locking knob without changing the telescope's elevation angle at all was tough. When I tightened, the star moved a lot. I needed that star on the east-west line since that was now defining the perfect mount altitude. I found myself doing only as much of a tightening as kept the star on the screen. Whatever way it moved, I then used the altitude adjustment knob to allow the mount to slip a little or push up a little, to get that star on the other side of the east-west crosshair line, so that the next tightening cycle was to bring it back to the line. If I needed to tighten more, I watched where it went and repeated the altitude adjusting so that in the end, the last final tightening of the locking knob brought the star to rest on the east-west crosshair. A bit maddening.
The Result
As a result of doing this test and making the adjustments needed to eliminate both stars from drifting, your mount is polar aligned. You could confirm it by repeating the drift tests with the mount's knobs locked down.
From this point, barring an incident of bumping your mount or loose knobs allowing slippage, any software that then tells you that you are not aligned is very likely deriving that inference from a less-than-perfect starting point, i.e., the part where it told you to put your scope in the Home Position. That is what was not perfect; if you've star-drifted, you're aligned. If you now run a Polar Align routine with software, when it tells you to do anything with your altitude and azimuth knobs and 'then press ENTER': don't touch any knobs. Just press ENTER and let it slew to its alignment star(s). The model will solve correctly.
Once upon a time, this was the way to determine the accuracy of your polar alignment. Now it is only a way. But it is a way that eliminates any other cause for a misalignment. It relies on celestial geometry, not pixel math or plate solving.