Can you identify this noise?

Wow, that’s a new one. Please let us know after you have it fixed. 

Does it have a battery for the RailSounds? It may need replacing.

If, as der meister states above, it's a matter of the handle not being completely in the 'off' position, suggest trying the following in an effort to confirm...

Next time you hear the buzz after moving the handle to 'zero', DO NOT touch the handle again.  Instead, pull the line plug, wait a couple seconds, and then re-insert the line plug.  If the buzz is still there, the residual voltage at the zero stop may, indeed, be a source of the problem.  In which case I defer to the ZW experts.  

Moving the handle in an attempt to repeat the phenomenon is changing too many variables, IMHO.  

Alternatively, if you have a multi-meter, a careful probing of the output terminals to the track...or the engine's track rails (center/outer)...with the meter on its lowest AC setting and without touching the ZW handle might give an indication of a remaining/stray voltage.

Hey, as long as you don't 'let the smoke out', you're safe....for now!

KD

Got the same problem with one of my ZWs; the right hand handle doesn't switch all the way off.  Will have to tear it down and fix the handle one of these years.

Mitch 

On my old ZW, I put a small piece of electrical tape over the first few "windings" where the roller was touching them in the "off" position.  Works fine.  I'm not worried about ultra slow movement when running conventional, and when running Legacy, it's all the way up to 18 volts anyway.

Common issue with residual voltage when the handle is in the off position. I assume others knew you have a ZW though I didn’t see anything in your post about which transformer you have. Even modern train set transformers like the CW-80 and other Lionel 80-watt transformers have this design flaw.

Volt meter will confirm it.

Do I need to do anything or is it ok to run the engine like this? Will it hurt anything?

 Thats debatable.  Running electronics with under voltage isn't ideal. The components usually handle it in stride, but on occasion outside the train world, I felt some chip issues had been accelerated by low voltage comming from other components or a bad power supply. Because of the variences in builds and components by manufacturers, I think it would really depend on the build in hand. That said, most of our trains are designed pretty well and with lots of on & off in mind, I think the risk is kinda low, but it is just an assumption; not practical experience or specific knowledge.

I.e., I'd at least look into achieving zero volts. Besides, knowing the condition of your supply's internals is a good thing and uncapping an old one is usually just 4 screws and lifting the cover to do it, so why not?

On leaky PW power it's time to look at the throttle rollers too. It make have trouble getting onto the "zero volt pad" with a bad roller. (Check they spin freely as they move too) Bad/missing rollers can damage a transformer winding beyond repair. Every bit of winding wear lowers the output too.)

So you all know. I am using an MTH Z-1000