There are many, many things that make a QB who he is, and have a large impact on his likelihood to succeed. Far too many to list, actually, but I'll list several of the major ones below and ask you to rank them from most to least important.
Arm Strength
Accuracy
Height/Weight
Intelligence
Mobility
Throwing Motion/Release
Vision
Competitiveness
Leadership
Character/Work Ethic
I'd also love to hear some reasoning behind why you feel the way you feel.
1. Intelligence - Dumb QBs don't survive
2. Accuracy - They have to put the ball where it needs to go
3. Character/Work Ethic - They can be as talented as can be, but if they do not put in the work, forget it.
4. Leadership - If they are timid and cannot lead, they are going to crumble playing the hardest position in pro sports
5. Competitiveness - They have to want to win and care about winning
6. Height/Weight - They have to meet some minimums, it is very hard to compete if they are too short and they have to make up for it with fantastic intangibles.
7. Arm Strength - I might have this one actually a little higher than I like. But not every team runs dink and dunk systems so they have to be able to make the throws. But, keep in mind, having a bazooka for an arm and that's all is not much good.
8. Vision - The player has to be able to see the field and develop anticipation.
9. Mobility - depends on what you are talking about. If it is "running QB" type mobility, not much at all, the team has to understand the handicap. But if it is mobility in the pocket (i.e. feeling the rush), then it goes much higher on the list.
10. Throwing motion/release - Can be corrected or even just left alone.
Some of these are closer together or could be listed as equals, but since you asked for the ranking, there you go.