Drop-shipping on sites where it's against the ToS for sellers is a great way to get fucked by buyers. Whenever a seller drop-ships a product to me when I order from a site, like Amazon for example, that doesn't allow sellers to drop-ship, I could in theory just claim I never got the product and the marketplace forces the seller to refund me. If the seller wanted to prove it was shipped and I was lying they'd be forced to reveal the product shipped from a Wal-Mart warehouse or something. If you're drop-shipping on eBay and having packages sent from Amazon, as I've seen done by morons, a disgruntled customer can out you to both eBay and Amazon and get your seller accounts banned.
Don't drop-ship, all it takes is one customer who knows how the system works to fuck you over.
edit: it's also a great way to get screwed on returns when somebody claims there's something wrong with the product. Ask them to send it back to the third party you had it shipped from, if that third party would even accept it, and the buyer can still escalate to customer service for the marketplace where they bought from you and fuck you that way too. Then they might not even send it back and claim they did. How are you as a drop-shipper going to prove it either way? What recourse do you have? I mailed a box full of dirt and gravel to Target returns once because I was sick of a Pajeet drop-ship scammer's bullshit. Wonder what they said to him when they opened that package.