I have a very old all metal light fixture with 6 small light bulbs. One of them is OFF when the others are ON and turns ON when the switch is OFF. There is only two wires going to the fixture and the switch is single pole switch. Is the light socket somehow miswired or shorted?

Is the light socket somehow miswired or shorted?
As the light fitting is still functioning, there is no short.
But clearly there is a problem with the wiring of the light fitting.

As the single light switches reciprocal to the single pole switch, the following has to be the situation :

The one single light is wired accross the single pole switch.

That way, when the switch is "off", the power is via the single lamp in series with all other lamps (which will produce a small fraction light of their full capacity. As a result the single lamp will burn nearly on full power.

And when the switch is "on", the power is directly via the switch to the 5 light bulbs and nothing to the single lamp.

Solution :

FIRST : pull the power plug.

All you have to do is open the fitting, check the wiring, and move the wire of the lamp that is burning odd that is connected directly to one of the powerlines to the other power line, and leave the other wire on the switch that is connected to all other lamps.

Success !

:)