I made this near black test pattern which might be more useful for getting repeatable results compared to using a scene from a movie.
The pattern consists of 12x12 blocks where each block is using one of the available video signal levels below 5% (assuming all valid levels run from 16 to 235). First column has background at level 16, second column has background at 17, etc. all the way to background of 27. The smaller inner boxes also run from level 16 to 27 as you go down each column. This covers every possible combination of near-black gray next to every other near-black gray.
What you would want in an ideal display is that each inner box is distinguishable from its outer background box. A set with good gamma tracking makes it easier to distinguish the boxes from their backgrounds. Only the diagonal boxes (running from top/left to bottom/right) should have the inner box matching their outer background box. The black surrounding the entire pattern (and entire the top/left most box) should not be visible since it's at video level 16.
If your set passes this pattern, then you are seeing all the shadow detail that is possible to encode into a BD disk. Well, at least in grayscale. We would need a different pattern to see if any near-black colors are lost.
Whatever remaining loss of shadow detail appears in real-world content would be caused by director intent or by limitations of our eyes. We can't simultaneously see dark and bright detail near each other. A higher contrast display like OLED makes this limitation more apparent.
You should do this with whatever ambient lighting you normally watch movies in. If watching in the dark, let your eyes adapt for 5-10 minutes.
It took a couple hours to figure out how do make this. Let me know if anyone finds it useful. I accept donations of unwanted OLEDs - just send a PM for directions.