Does an aircraft like the Airbus A-320 have external sensors to detect damage to the aircraft?
This is related to an answer I gave here about why aircraft typically do not have mirrors and external cameras.

Short answer: yes aircraft do have sensors to detect damage, but not the kind of damage you're talking about.

Long answer: to design or decide what sensors to put on the aircraft and where, we have to get started with failure modes. There are at least a million way for components to fail, however, some failure are more likely to occur than others.

Do we have sensors which detect failures / abnormal situations? We do! We have sensors for control surfaces, hydraulics, gears, tire pressure, cabin pressure, engine temperature, oil pressure etc. 

Here is an image of one of the cockpit screens on a Boeing:


(source)

OK, so why not more sensors?

Because sensors can fail. Now that would be a nightmare to troubleshoot: the sensor says the right outer landing light is not illuminated. Is that true? Let me exit the aircraft and take a look......

It turns out that:


Many failure modes are "internal", e.g. a valve malfunctioning. They are invisible on the exterior of an aircraft.
Aircraft rarely collide with any other objects.
Relying on visual indication is actually a good thing, because it is reliable and it's free.
Building an array of sensors covering each skin on the aircraft would be extremely complex, the construction cost would be high and the system would be heavy.
Sensors are just another component of the system. The more sensors, the more likely something will fail. At some point one has to trust the underlying component to function without relying on system indications.


Perhaps this is the kind of system you have in mind:


(Screenshot of "Stealth" (2005), 01:01:11)

Nah, that's just Hollywood artistic license.