I configured it to sell green/blue/purple items, but they aren't selling.
There's probably a Keep Rule blocking it. Open the rules dialog (/vendor rules), and click on the "Keep Rules" tab. By default, we enable a Keep rule for Soulbound Gear and Uncollected Appearances. Keep rules always run first as a safeguard. Use care when unsetting them, and be sure to check out your inventory items afterwards to make sure nothing you care about is marked for selling. If there is, you can add it to the Never-Sell list using the mouseover keybind, or by using /vendor sell never <itemlink> in the chat
When I mouse over a bind-on-pickup item I don't yet have that is an uncollected appearance, Vendor tells me it will be auto-sold! What's going on?
The uncollected appearance keep rule only applies to Bind-On-Equip items. Bind-On-Pickup items will grant you the appearance on pickup, therefore it is safe to sell once you have that item in your possession. Vendor is doing the right thing here, even though it might not seem like it.
I accidentally sold a bunch of my gear and I can't get it back!
Okay, no one has really had this problem that we know about so it really isn't frequently asked, but we figured it would be worth describing means of recovery just in case it does happen. There's two options. One is the buyback cache. If you go to the merchant and click the buyback tab, you can buy back items you have recently sold. But it only tracks the last 12, and clears when you log out. The other option is Blizzard's Item Restoration, which allows you to get back all sorts of stuff you may have accidentally removed. But you can only do it once every 15 days. Be careful when disabling Keep Rules - they are there for a reason!