It has been claimed several times e.g. [here](https://physics.stackexchange.com/questions/41090/is-time-the-rate-at-which-one-moves-through-space/41097#41097), and [here](https://physics.stackexchange.com/questions/148306/proper-time-in-general-relativity/148313#148313), also [here](https://physics.stackexchange.com/questions/53334/why-do-clocks-measure-arc-length/53361#53361), or (outside PSE) [there](http://en.wikipedia.org/wiki/Clock_hypothesis) that 

> 
> *Clocks measure proper time.* 
> 
> 
> 

Or equivalenty:

> 
> *proper time is just the time that would be measured by a clock traveling along that timelike curve as its world-line*
> 
> 
> 

Or in short:

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> *clocks measure arc-length.*
> 
> 
> 

All these referenced claims are apparently without any further qualification of the clocks being considered. In particular, there is no recognizable mentioning of clocks having been "good" (as opposed to having been "bad") in the sense of MTW §1.5. Therefore I like to know:

Do all clocks measure proper time, **including bad clocks**? 

(When answering, also consider applicable follow-up questions such as how "good clocks" and "bad clocks" ought to be distinguished experimentally, at least in principle; or which definition of a "clock" would include "good clocks" as well as "bad clocks".)