Should there be continuity between brush contacts on an AC motor rotor?
The two tests you do on that type of motor are "180 degrees" and "bar to bar".  You have to measure the two pads that are 180 degrees apart.  Measure each pair of pads around the motor and see if any of the measurements are a lot different than the others.  It doesn't matter what the measurement is, it should just be consistent.

The bar-to-bar test is the same.  You measure two adjacent bars all the way around the motor to see if any of the measurements are a lot different than the others.

All of the bars having continuity with each other is not an issue, but a third test you can do is to make sure that none of the pads/bars has continuity with the outside of the armature (the larger diameter portion in the middle of your picture).