We refinanced our mortgage through an online lender at end of last year. There were no problems with the process, as long as you have a scanner, credit card and email address. Do have all your paperwork scanned (pay check stubs, SS cards, drivers licenses, etc.), as it speeds up the process. Likewise, you'll need to scan and send back their documents that you sign. CC was to pay for the appraisal, and that was done over the phone, as was other conversations. Closing was done at a local title company and we had to scan and email them an "as-built" survey that we had from the original mortgage (to avoid a delay in the process).
There were absolutely no problems with the whole process. We were able to get a discount against the fees, so we only had to come up with the required escrow amount plus appraisal fee. I believe I found the mortgage company through bankrate.com, but the company only does business in our state.