Does computational complexity theory take into account problems with subjectivity in the verification of a solution? When we discuss P vs NP we are looking at the difference between problems that are easily solved versus easily verified (wrt polynomial vs exponential time). 

But in both cases these are black-and-white results. We do/don't solve the problem, we do/don't verify the problem. 

What about cases where there is subjectivity to the verification? Problems where 2 people don't agree on the solution, since the solution may depend on context, environment, etc.

Does computational complexity deal with the subjectivity in verification, or are all problems modeled as black-and-white results?
No.  Computational complexity doesn't deal with subjectivity.  In computational complexity, we consider formal languages that are precisely defined, so there is no subjectivity.