We just purchased our house-28 years old, bungalow, and when we run any hot water-shower, or taps shortly after we can hear a dripping noise from in the wall. Is this cause for alarm or what should we do?

Yes, more than likely cause for concern. Too much of it could result in quite the overhaul of floor/subfloor... possibly even structural (floor joists/bottom wall plates etc) damage.

[QUOTE][when we run any hot water-shower, or taps shortly after we can hear a dripping noise from in the wall/QUOTE] Unless you can see water coming out from the wall I don't think you have a leak. I think it's contraction and expansion.
Knocking, popping, creaking and crackling pipes are a common complaint, especially in colder weather. I can tell you what's happening and take the mystery out of it but you're not going to like the repair. When a draw is made on a hot water line the line expands against a pipe strap next to a stud and when you drain hot water from your tub or shower it goes into a chase that is a little cooler then room temperature. The heat expands the pipe causing it to rub against the stud to which it is pipe strapped. This is the sound you hear. As it cools it contracts and the noise is heard again. To repair it you must tear open the walls and locate the pipe strap that's causing the problem and shim it tight. Most people when they learn what causes it just elect to live with it. Good luck and thank you for rating my answer. Tom