I had a very poor experience with Verizon "certified" refurbs. I bought 5 iPhone 5 16gb phones in the past. Ultimately, I had to go through 10 phones to find 5 keepers. And the issues were not minor/cosmetic.
1) The very 1st phone I opened...the home button was "stuck". It literally would not move when pressed. Of the multiple replacements, another one arrived with a suck button as well, so 2 of the 10 of them.
2) I ran battery tests on all 10 phones. Some were brand new batteries, but 3-4 of them were run down to about 65-70% of usable life. (I am typing this from memory, but several of the phones were down to about ~1,000 from a top of ~1,400).
3) The microphone on 1 was blown, so the only way to make a call was with a headset or via bluetooth.
4) 1 had an obviously replaced screen and was not properly aligned (so badly that it would not properly fit in a case). When touching the screen, even lightly, you would see rainbows all over the unit.
There were other issues, but these are the ones that come to mind. So again, I bought 5 phones, went through 10, and even of those replacement phones I had to accept some that had issues (but not serious enough to send back again and again).
I would not buy Verizon refurbs again.
Oh, and Verizon said that their refurb phones come directly from Apple. I absolutely do not believe that for a second.