Customer orientated thinking - especially in terms of music. eg: "What would the audience like to hear next?", NOT, "what would I like to hear next?". This way of thinking also, goes hand-in-hand with "What would the audience think of what I'm about to do next?".
Business orientated thinker too - OK, so Mr and Mrs Smith have just paid us their weeks wage for a disco (thanks!) but keeping up the professional image until the last van door is locked is a good idea - you never know exactly when the venue staff stop assessing you and your trainees - answering a call of nature behind the fire exit door might not get you future bookings.
Music knowledge - (!) Not the sort of trivia about how the drummer of that band is now the half-sister of the lead guitarists second cousin of the guy that used to play the bongo's for the guy with the beard in Genesis... but at least enough to know that they need to quickly ask "which artist?" when someone comes up and asks for something like - "The power of love"...
Sense of humour! and not mic-shy - not for "Tony Blackburn" style announcements between each track, but someone who wont stand there all night claiming "I'd rather let the music speak for itself" when you ask them to dedicate a song, or thinking that the mic and its lead, are mearly plugged in to keep the dust out of that XLR socket. I visited a disco about 4 weeks ago and the DJ said "Hi yer everyone", "Last orders", "g'night" and that, was about the total sum of his vocal enticements...
A Think-on-their-feet person.... if "Item X" stops working and the theres no workable spare - theres got to be a way of getting "item W" to work with "item Y" (safely) to keep the show going.