Should I give out references to an employer I am not that interested in?

Hold your references until the prospective employer asks for them. Remember that any reference you list on your list of references is assumed to be positive. But prospective employers don't stop there. 

Ever wonder why an application will ask you the question "To whom did you report?" That's because those are the most important references that a prospective employer wants to speak with. 

Remember, your reference list is nice, but it's not the end of the road for a prospective employer.