I'm simply a co-op engineer working with other engineers, but the two attributes I've found to be most important in other engineers I've seen are humility and dedication. If you have graduated with a BS, it proves you can figure out the types of problems you're given. But it doesn't necessarily qualify you as a 'team player'. The engineers I've seen who are willing to help others, take criticism with a positive attitude, and work hard seem to be the happiest and succeed the most. That's just what I've seen, anyways. And they're the ones I like spending the most time around, and I ask them questions when I need help. The 'sensitive' or 'touchy' engineers who refuse to take correction can be very difficult to work with.
EDIT: I listed these two attributes assuming one has at least decent capabilities in performing one's job. If an engineer can't use a computer, calculator, perform basic to intermediate math, or be able to analyze a system or problem then it's going to be difficult to do anything as an engineer, really.