Hi AJ, Devin and Ko make excellent points. I agree with Ko and Devin, once you make a selection, stop shopping around. Making a switch will be confusing to your transaction team (i.e., attorney, buyer agent, title, etc.) and may result in delaying the closing.
In addition to their responses, while you are performing due diligence, please do understand that the cheapest rate doesn't always equate to the best overall deal and/or best service. For example, (1) are you being charged points for your quoted rate, (2) do you get a no-fee interest rate float down after locking, (3) does the lender offer a no bank fee refinance service in the future, etc. Service can be measured primarily in the lender's responsiveness (especially during the week leading up to the closing).
Lastly, lending requirements vary from lender to lender. (Yes - even for conforming products.) Recently, I had a borrower (who worked for this large bank) receive extraordinary lending requirements resulting from the lender's appraisal report. This large bank is obviously looking to reduce their risk and possibly the deal. If this borrower went to almost any other lender, this bank's repair requirements would be a non-issue.