No perfect continuity between any spot in my Fender amp chassis

[slidincharlie (Carlo P)]

My SF Vibrolux Reverb amp, which I use very rarely, has some hum with no guitar plugged in. The hum increases when I turn up the volume pot in either channel. Also, the hum disappears when I touch the chassis but increases when I touch the Bright slide switches. I guss it is ground hum.
First thing I checked for continuity between several grounded points in order to spot any bad/defective/dirty ground solder. To my surprise I never have 0 (or close to 0) ohm readings between any point, even between adjacent points on the chassis itself. I never have readings below 7-8 ohms.
Why is that? Shouldn't I get 0 or close to 0 ohm readings between points at say 1 inch distance on the chassis?
Do I have a serious grounding issue?
I am using a Fluke DMM. Could it be in need of calibration? is there a way to test its precision? Maybe it needs new batteries?

[Helmholtz]

Short your meter leads and see what resistance reading you get.

Also check the meter battery.

[slidincharlie (Carlo P)]

Shorted leads read about 0.3. Made new readings, which look ok now. Maybe random bad lead contacts during previous readings? I have changed the battery anyway, I haden't changed it in years. Thank you.

[Helmholtz]

Are your input jacks switching/grounding?

Cover the amp chassis with a grounded metal plate or aliminum foil for shielding, any difference?
The amp cabinet should have a shielding mesh inside (top side).

[Jon Snell]

Fit a 3 pin plug if it hasn't already got one and do the usual ... bin the death cap.

[loudthud]

The banana jacks on a Fluke DVM can sometimes become high resistance. Simply rotate the plug while it's in the jack hole to refresh the connection. The leads also wear out. You have to find where the resistance changes as you flex the lead, then shorten the lead to bypass the bad spot.

[slidincharlie (Carlo P)]

The ohm readings were bad especially at the Normal channel jacks. I have disassembled all input jacks and cleaned every part with fine sand paper and steel wool, especially where the shorting ends touch. There wasn't evident rust or dirt, yet the readings are now very good and the hum went down a little.
I will check carefully the meter's leads, plugs and prongs anyway.
Thank you.

[Mick Bailey]

Even a microscopic oxide layer on otherwise good looking surfaces can act as an insulator. My Fluke probes are hardened and are very sharp, but even so, sometimes I have to scratch the surface to get a true reading if I'm suspicious of an initial overly-high reading. Older Fender amps can suffer from raised resistance between sockets and chassis, as well as the shorting contacts. Also don't forget the barrel of the input sockets - these can oxidise too. I use a piece of fine Scotchbrite in the bore to brighten them and a squirt of contact cleaner. The trick is to only to clean the surface not to scratch or remove the plating.