Is it possible to measure the differences in processing and interpretation of reality between individuals? What variables can be measured to compare, for example, two different individual's conscious processing and interpretation of the same objective reality ? For example, when terms like "distorted view of reality" are thrown around, how does one measure that or can conclude that?

How can we measure the differences in the processing and interpretation of reality between individuals and if it's impossible, please explain why it can not be done or what can not be measured.
The answer to this question is rather philosophical will mainly depend on who you ask.

If you ask someone who is close to physicalism, he would probably respond that there exists nothing that cannot be measured, hence, differences in the processing and interpretation are measurable in principle too, although we might lack the necessary apparatus and methods right now. 

However, if you ask some who is closer to dualism, he would probably respond that there are (at least) two kinds of consciousness: access-consciousness (or a-consciousness) which can be measured with scientific methods, and phenomenal-consciousness (or p-consciousness) which is only accessible to ones own mind and cannot be measured by scientific methods in principle (cf.  the hard problem of consciousness). 

Please note that this answer is a simplification that gives only a glance into a debate that filled volumes (cf. http://en.wikipedia.org/wiki/Philosophy_of_mind)