I can think of a few right off the bat :-
(1) Design and usability of website
(2) Promotion and getting eyeballs - getting visibility for your e-commerce operation
(3) Scalability (just in case your website actually becomes popular)
(4) Ensuring consistent fulfillment processes -managing orders
(5) Ensuring credit card security and foolproof and robust interfaces with credit card and payment merchants
(6) Managing tax calculation and compliance to government rules
(7) Managing shipment - carrier services..choosing best carrier and figuring out how much of the cost (and more) you want to pass on to the customer
..think above starts to scratch the surface of some of the challenges an e-commerce vendor may face