We've just purchased a new washing machine, and in the process of taking the old one out, we've come across a problem. The hot water hose sprays and drips as we try to unhook it from the machine. This is after we've turned the hot water shut off valve, off. Is this something we can fix ourselves?

Older style valves had faucet washers and the hot is usually the first to go bad. Try turning off the valve at the HW heater and release pressure in another faucet. You should be able to now change the hose. However, I would disassemble the valve and see if the washer is bad. I have seen them completely missing.