What does "veridicality" mean in terms of psychology?
Veridicality is a term used in cognitive science; it is the degree to which your internal representation of the world accurately reflects the external world.
Some background
Since the work on Humberto Maturana in color perception, it was considered very important to not always focus on the fact that there is some external stimuli to be cognized by the subject and then reacted on, but that instead there is an internal world or representation which is then cognized and responded to. In many cases the veridicality of the internal representation is very good, and the experimenter can focus on just the easy-to-observe external stimuli. However, in many settings (like color perception) the veridicality of the internal representation is low (easiest way to imagine this: think of a difference in internal representation between a color-blind and non-color-blind person). Hence the experimenter needs to explicitly measure the internal representation and try to understand how it acts. Once you have a measure of this (a 'criterion for veridicality') then you can start to think about how the subject cognizes the stimuli.
Specific to this paper
In the context of the first sentence, what the authors are saying is: even with the narrow focus, it appears that the accuracy of the internal representation does not improve. Thus, the experimental results depend not only on the external stimuli (psychophysical method used) but how good we are at estimating the accuracy of the internal representation (criterion of veridicality).
In the second sentence they propose a metric of veridicality: ask how far you think an object is (say in meters) if the results scale linearly with actual distance, then the internal representation of space is good, else it is not.