When the video starts the Flight Management System (FMS) screen is  running a standard iterative "Position Monitor"  display.

There are actually three independent position references used, and shown on that display labelled FMS1,  FMS2, and GPIRS.  In principle they should all agree exactly -- in practice to within 0.1 arcminutes.  If you single-step through the video you will see that pretty much  the case -- in Latitude -- but notice the MUCH larger discrepancies in longitude, which  grows larger with successive screen updates.

The 4th line (MIX IRS) is a (weighted) average of the three.

Below that 4th line, where the display text says NAV (3 times), that gives the closing distance (in  nautical miles) to a reference programmed waypoint (90N in this case).  You can see the IRS1, IRS2, and IRS3 solutions from the three references  do not quite agree; part of that of that is that they actually are slightly  asynchronous updates (but the amount of asynchronicity is [or should be] known to the FMS software).

We were doing a slow overflight - with a ground speed of 257 nm/hr.  So, when we were about half a nautical mile out (about 7 seconds flying  time), I switched over to video the "glass cockpit" compass display.   On that display, the yellow stick-figure of an airplane at the center of the navigation arcs represents the position of the airplane.  The two dashed arcs represent  distances of 5.0 and 7.5 nM from its instantaneous location.  The outer  compass rose is 10.0 nm.  The green diamond is the projected preset target position of the aircraft (8950N)  and "heading" , at +10 nm from its current position.  The green solid line represents the aircraft's  projected flight vector.

NOTE THE YELLOW WARNING (which was flashing, but was not picked  up as flashing on the video because of the frame rate) that says  "CHECK HeaDinG" as the outer azimuth circle is spinning around!  Also (for later reference) at the start of this video segment our ill-determined  "heading" is appx 95 deg "true", as the compass is spinning around. 

As the "green line" disappears (the display SW could not calculate a heading),  and as the video zooms out, we were 10.1 nautical miles from the "10 nauticla mile  from Pole"  position - which you can JUST read on the upper right as the display blanks out.  The airplane icon then disappears and the display blanks out as we cross the "Where the hell are we {in longitude}" singularity.  

As we cross the North Pole (and as Sebastian sticks his finger in front of the display!),  the display S/W begins to recover and rebuild the screen.  Note right after  the offending finger is removed the distance from target goes from 10.1 nm  to 10.0 nm (as it should right at the pole; but actually with a six second  delay), as the compass continues to spin...

Neat!, eh?