The house we just moved in to has a sign on the front of the dishwasher reminding the operator to turn on / turn off the water supply to the dishwasher under the sink. Is this overly cautious or a sensible precaution?

Only if the solenoid valve in the dishwasher was leaking and not shutting off completely.

I've never, EVER had to turn off the water to a dishwasher between uses in the last 40 years I have been around them.

I agree, no need to shut water off if the unit is operating propertly. Try NOT shutting off the water and carefully observe what happens over an hour or two

I also agree with previous posts...

The dishwasher had a problem and the owner went the cheap route instead of having it repaired. As a renter you should expect all fixtures and appliances to be in working order, Having to turn the supply off and on does not indicate a working appliance. It should be repaired at the owners expense. Let us know how you make out. Good lick, n Tom

Thanks Tom, I'm actually the new owner. The previous owner has done a number of "energy saving" fixes that we've been finding throughout the house; some make sense, some don't. I've left the water supply on for the last several months, while using the dishwasher regularly, and there is no sign of any leaks.
Tabitha

Tom's not around right now, Tabitha, but thanks for taking the time to update the thread!

Mark