Three qualities that DJs should strive for: flow, range, judgement.
Flow (in DJing, not psychology) is the ability to smooth the transitions from one song to another. Rather than making big jumps in tempo, style, recording quality, or feel, a DJ who flows chooses songs that resemble each other enough so that dancers don't look up and make confused faces or shoot dirty looks at him. Instead, the songs should make sense one after the other--they should sound like they go together. I think pop radio DJs aim for something similar (to the extent that they are humans rather than computers), and club DJs take flow to the extreme, mixing one track into the next to create a seamless transition with no dead time.
Chicago DJs generally take the concept of flow very seriously. One of them once put it to me that the difference between a DJ and someone who "just presses play" is that the DJ flows. (I would add to that: a DJ also has range and judgement.)