I'll second and third resourcefulness, news awareness and particularly curiosity. I wanted someone who wanted to know more.
I'll tackle the radio side, because that's where I handled the majority of my hirings.
Just like your best five clips in print, EVERYBODY worth hiring in radio should have a killer air check. If you don't, you'd better get one, because while the resume tells me what you've done and where you've been, that alone won't get you a face-to-face with the news director/program director/station owner.
I'm listening for the right "sound," which is unique to every position, regardless of gender, racial makeup, age or experience. A morning drive co-anchor for a news talker is going to sound different than a lifestyle reporter for an easy listening station or someone holding down the evening/overnight shift on sports radio. I'm hoping to pair voices to complement my existing staff. Authoritative? Pleasant? Knowledgable? It's not always a radio voice like John Facenda that is required, as much as someone who interacts well with the target audience.
Back then, I had an entire afternoon to screen applicants, so in three hours, I needed to have a good handle on what I could expect: How would they represent the station? How well would they take criticism and suggestions from me? How well would they interact with the rest of the staff? And perhaps most importantly, how much potential was there for them to grow and prosper in this particular job? Did they show curiosity?
Depending on the position, I made sure to "role play" with each applicant, with the idea of learning more about how they thought on their feet, how well they maintained their composure and how they sounded in real life situations.
If they wanted to anchor, I'd have them read that morning's newscast for me, PLUS then ask them to ad-lib from a made-up scenario (accident, fire, election results, weather situation) where I gave them a limited amount of information at first and add to it as the simulation continued. That's a skill you can only acquire from experience.
If it was play-by-play, I'd have them do any game or sport off the top of their head leading up to a commerial break, just to hear their cadence and clarity. If it was for a call-in show, I'd act as a caller and interact with them to see how they dealt with the audience and how well they stayed on topic and kept the conversation moving.
Sometimes you immediately know you've got the right person. Sometimes you never find them and have to make a choice based on your instincts. Many times, you know the person is overqualified for the position and won't stay long because they'll move up quickly. Other times, you may see potential you might be able to tap into.
It's never an easy "one size fits all" situation. I've had the "perfect" candidate flop because she suddenly had an unexpected case of mike fright once she was alone in the studio. I've also hired kids right out of college who went on to anchor in Los Angeles.