PID measurement and control different scales
... how to handle the measurement data versus the control (reference value).


Usually in a single-input single-output system your reference value, the one you want to achieve, and the measured value from your sensor should be in the same "unit", so when you write code to acquire the value from the sensor you can either convert it to actually intelligible units (V, m/s, ⁰C and so on) or use them all as plain bits. Converting them to the actual units is more intuitive and better to learn with. But eventually just using the actual binary value will be as easy to work with and will incur less numeric errors. 


  For example, say my feedback is measured with a 10-bit ADC. My control is a PWM with a valid duty cycle range for my application of 55-172. Do I scale linearly between the two ranges? Say my target is 756 ADC. I would set my PWM to 86 initially?


The range of the actuator (the PWM) will not change how you calculate the error, but, as you suggested the PWM having a valid duty in a certain range is a nonlinear problem such as integral windup, actuator non linearity  and  many more. I would suggest that you make the control signal, "the duty", something such as,

$$ u_{PWM} = u_0 + u(t),$$ 

where \$u_0\$ is the value that is either: 


in the middle of the range, or
the common value during the operation of your system, or
a PWM that you know to cause vary little change in the system.


And \$ u(t)\$ is the control signal that comes out of your controller. For the PID case I would keep this as just the result of the PID itself. Though it is possible (but I do not recommend) to try to deal with the non linearity of the actuator by using some wacky function that makes the actuator have a "linear" response proportional to the PID controller output.

All those choices of \$u_0\$ can lead to different startup behaviors, so you should carefully evaluate the constrains you need to follow, overshoot limit, settling time and so on.


  Should the error calculation take place in the ADC range or PWM range?


Whether you are using the raw ADC value or converting it to some unit/measurement you should use that and not the PWM range. 


  What if the PWM control was not linear?


Then the PID might solve your problem but the analysis of nonlinear systems is way more complicated, and using the linear PID (control theory) will only get you as far. What people usually do is:


Linearize around the stability point, get an approximate linear model and keep it stable at that point (and close to it!), with the actual startup control that takes the system to that operating point being different then the one that keeps it at that point. Or,
Have a controller that adapts to different points of operation, let's say that you make a PID that re-tunes every time it gets "far" from the previous linearization.