I've seen some banks that were higher and others that offer pricing that couldn't be matched. One in particular that paid for all of my buyers closing costs and the rate was still below anything that I could find available. I was skeptical that it was true till it closed.
I like to work with loan officers that I've done business with but if my clients want to shop around I tell them to check with their banks as well.
If you trust your real estate agent, why wouldn't you trust their recommended lender?
Successful agents have a successful business network.
You should be presenting all your questions to your agent's recommended lender while you sit side by side with him/her.
A little more of APR: http://www.trulia.com/blog/elliott_r_oliva/2011/07/what_is_a
Also keep in mind that not all lenders rates move the same amount each day, you may see one lender trying to curb new business (perhaps volume is too high for their service standards) and not improve interest rates as much as their competitors on a day that interest rate pricing is improving... thus if you based choosing that lender because of their lower rates, and later on in the process the rates are the same as competitors you may feel cheated but it'd just be because lenders become more/less competitive depending on when they need to be - and mortgage brokers broker loans to those same lenders so their clients aren't immune either.