[Mondial]

Yes, if you are receiving stations with the antenna connected to the grid cap of the 58 mixer/oscillator but not when you connect it to the antenna terminal, there is a problem with the antenna coil or associated circuit. You might check the .1 uF bypass cap connected to the cold end of the antenna coil secondary. If it is open, the coil will be floating with respect to RF ground.

As far as the detector screen voltage, 140V is about what I would expect there. Remember, the 57 is biased at cutoff, so with no signal very little current flows in the screen and plate circuits. With very low screen current the voltage will rise, only limited by the 3 meg series resistor. I would not take the voltage measurements too seriously. The voltage chart shows different screen voltages on the 58 mixer/osc and the 58 IF, yet the schematic shows the two tubes screens tied together, so how could the voltages be different?

Assuming the schematic voltages were measured with a voltmeter with a 1 mA meter movement typical of the era, with a 500 V full scale range the meter input resistance would be 500k. If you try to measure the screen voltage at the 57 pin, you are creating a voltage divider consisting of the 3 meg resistor connected to the 260V supply and the 500k meter resistance. So even with the tube out of the socket you would never measure more than 260V x 500k/3500k, or about 37V at that point! This is a worst case situation, as most measuring points do not have a 3 meg source resistance, but it does illustrate that unless the type of meter used is specified, the voltage readings are questionable at best.