How predictable the rod is and ease of use at say 20,50 and 70ft.
For me turning over a long leader is important as is pick off with a long line. Some top end rods IMO are incapable of lifting a long line with one back cast and the shooting. Something i do often given the way i fish.
I guess it has to do what you want without you having to think about it but Grouse is right, i am not sure for me anyway there is "one" rod. In the hight of summer i want something gentle and delicate and at the start of the season i want something that can punch through the wind and get the fly on the other bank if needs be. Where i do disagree with Famous is that it has to suit your style,like it or not i have a casting stroke that is ingrained and regardless of tuition to iron out any problems its mine and i am stuck with it so the rod has to allow me my foibles. Thats not to say it has to be just fast or slow good rods come in many guises.
So to answer your questions:-
1) I look for a rod that suits my casting style, does what i want it to without having to think, turn over a long leader, lift off a long line and shoot with only one back cast.
2)Criteria is an odd one. It involves so much more than the performance of the rod. The tube, the sock, the colour of the blank, the reel seat, hell the name of the thing might influence whether i pick it up or not. The criteria is there fore do i like it and need it
3) My favorite rods are effortless,efficient, have soul, feeling and do as i want. Some of them have their faults weather is poor cork, a **** coloured blank or a poor reel seat but they all perform as i want and ask of them.
In summary i suppose what i look for is the words "Streamflex" on the blank