Luke wrote:

Our TV reception, from a roof antenna, was intermittently
flaky. Trying to find the problem, I got a shock when I
touched both the TV F-connector and coax cable antenna
lead. So I put a tester on and to my surprise got a 75 volt
? reading.

It's also 75 volts between the TV F-connector and the
outlet ground plug hole or outlet screw. And, there's
75 volts between any connector on the TV and any of
these grounds. I'm also getting ~40 volts off the VCR
F-connector, and ~50 volts off the DVD player *housing*.

Best I can determine this is the case with all house
circuits. I plugged the TV into several, using extension
cords, and carried the DVD player around to plug it into
all circuits. I also get ~30 volts off the housing of
an old stand mixer in the kitchen.

The voltage on the mixer points to a household wiring problem, and the
floating neutral makes the most sense. Get it fixed.

Voltage on things like TVs and VCRs is often normal (but probably not
in this case) because of low-value filter capacitors connected between
chassis ground and the AC lines. These capacitors are small enough, no
bigger than .005uF each, to limit 60 Hz AC current leakage to safe
levels, just a few milliamps. There's also a low-value capacitor in
series with the F-connector's center pin, also for safety isolation,
but TV power supplies usually provide no isolation and have the TV's
chassis connected directly to the neutral wire (why TVs came with
polarized plugs long before most other appliances did). Sometimes the
chassis is even held above ground, at 60-90VDC (be sure to measure with
your meter set to both AC volts and DC volts).

I don't understand why your TV antenna mast and cable aren't grounded
for lightning protection and to prevent shock (any dead birds or rats
around the antenna?). However in this case that could have caused
damage to your video equipment.