Is the professor's reputation taken into consideration by the admissions committee when they read her/his recommendation letter I worked as an RA and a TA with a professor, therefore I am  hoping for a solid recommendation letter. However, I am concerned if the admissions committee would run a background check on the professor who wrote the recommendation letter, mainly:

1) Would they be looking at the students opinion of that professor? Examples of student's opinions can be found at websites like ratemyprofessor.

Or 

2) Will the admissions committee just check his research history and research related accomplishments?

And if they found something like bad student ratings, or a gap in the professor's research history, how would that affect the recommendation letter he wrote on my behalf?
While the idea of basing any important decisions on ratemyprofessor reviews is laughable, the answer to the spirit of your question is yes. If someone's writing a letter about your research, their reputation as a researcher matters a great deal. How am I supposed to judge someone's research potential if I have none myself?

As for teaching recommendations, in my field (math) this depends on what kind of position you're applying for. Having a teaching letter from someone in a teaching-oriented role (like a calculus coordinator or, if you're lucky, the Director of Undergraduate Studies) is always nice, but this matters a lot more when applying for teaching positions. In fact, I've heard that teaching letters from research superstars (or people who aren't specifically known for caring about teaching) don't get you very far at small liberal arts colleges.