[MrFixr55]

HI DM Blackburn,

If you have disconnected ALL connections from the tuning cap, there should be NO continuity between rotor and stator OR between different stators.  The rotor is in continuity with the tuning cap (capacitor) frame which is grounded to the chassis.  Review the following link to the schematic:
https://philcoradio.com/library/download...l.%201.pdf

and the following isolated section of this diagram:
   

If you are measuring the tuning cap "in circuit", the oscillator section (green circle) would register open circuit, as the coil associated with the tuned circuit has a cap in series with it, therefore you will not see the coil resistance across the stator.  The RF Amp section (orange section) will have a high resistance as there as about 2.5 megohm between the antenna coil secondary and chassis ground (the AVC circuit).

However, the middle section, (red circle) the mixer section will have a very low resistance to ground as the secondary of the mixer transformer (the transformer between the RF amp and mixer) is directly across that section of the tuning cap.

To accurately test the cap:

• Label and disconnect all connections to the tuning cap.  (Grid leads can remain soldered to the cap but removed from the tubes.)
  
• Set the tuner to the highest frequency (rotor plates completely unmeshed with stator plates).
  
• If clip leads are available, clip the test leads of the DVM to the cap frame and the first stator section.  Resistance should be infinite.
  
• Rotate the tuner through its entire range.  The resistance should remain infinite with no "jumping" of the display.
  
• Repeat the test for the other 2 sections of the cap.
  

It is not uncommon for the plates of a tuning cap to oxidize developing what would look like little stalagmites and stalactites on the surface of the plates.  These will touch and short the rotor to the stator section in question.  In addition, mishandling of the tuning cap will bend plates, causing them to short together.  This is the reason that you want to start the test with the cap set to the highest frequency and the plates totally unmeshed.

Also please note that you are dealing with a somewhat troublesome vintage radio.  The RF transformer and Oscillator "Tickler" coil are notorious for opening in these radios, requiring you to rewind the offending coil.  

Hope this helps.