What do hiring managers look for in potential employees?

Will this person fit the Job (Education, skills experience) and the organization (organizational culture)

1. Competences
2. Expirience
3. Character
4. If he/she fits in the Company Culture

1. Education.

2. Experience.

3. achievement.

Experience !!!

Simply and practically ... they look for "what is required in the job itself"  and "what it takes the successful candidate to get the job done"  

They will not necessarily look for a superman or a guru or a wizard to do the jobs that do not requires these things to start with.

Having said that,   there should be a JOB DESCRIPTION  developed by HR in association with the target FUNCTION/DEPARTMENT where the employee will work.  This job description will be the basis for the selection process,  Along with that there will be the general ORGANIZATION VALUES, ETHICS, NORMS & BEHAVIORS  that employees should have anyway .

As a hiring manager ...

1. I will NOT hire the best talented person to a boring, repetiive clerical work, and I will NOT look fo an MBA or PhD degree holder to be a receptionist or telephone operator or driver or any other low entry job. 
2. The technical person should have product knowledg, lots of technical skills, and little bit of industry knowledge where the product belongs. 
3. The sales persion core competency would be selling not product knowledge,   Additional required areas would be industry knowledge (more than the technical person) and market/customer knowledge
4. The receoptionsit at the front-desk needs to be good-looking, well-dressed, cheerful/helpful personality .. and not a genius in maths or science or technology or selling
5. The telephone operator does NOT need to be good looking, a good voice will be enough, acoompanied by good company knowledge to know where and who to refer the callers or transfer the incoming calls to

These are just examples and I hope they give you the answer you want from my own view since you aksed for our opinion on this subject