I'm really wondering about my father. He's always been a bit of a hypochondriac, so it's hard to tell when something is real or imagined. Lately he's been complaining about neck pain that goes down his arms. He drops things like cups and glasses. He seems to be tripping over his own feet. Even though he's 71-years old, I've never seen him do this before. Could this be all in his head like so many other problems he's had?
People who have a pattern of getting attention through various imagined (and sometimes real) aches and pains are a challenge. As you say, it's difficult to know when to respond.

As we age, the chances of really developing something with serious consequences increases. Your father's age is a red flag all by itself. And the fact that he's developing new symptoms he hasn't had before is also important.

A visit with his primary care doctor is probably in order. If your father's symptoms are psychologic in nature, the results of sensory or motor tests will be negative (normal). A simple X-ray of the neck and spine can give the physician quite a bit of information to help sort out the symptoms.

If finances are a concern, there are a wide variety of tests that can be done by the doctor with your father in the office that don't cost extra. It's probably time to take a first-look. The fact that you're concerned tips the scales in favor of an exam at this time.