I had one of these grills for many years... the flaking black stuff inside is seared grime, not paint. It happens. I wouldn't use oven cleaner on it -- just wire-brush it every now and then so that it doesn't drop little black flakes on the food. No need to paint inside the grill.
These are excellent, excellent units, by the way... weak spots IME tend to be the hardware that holds the carts together and the drip tray racks on. I gave mine away after the cart collapsed on me last winter, but it was used hard and never covered year-round for 9 or 10 years here in Massachusetts, so rusty hardware was no surprise and no knock on Weber's quality. If your cart is in good shape you've got many years of great cooking ahead of you.
One other thought as you go shopping for grates... many folks will recommend the stainless steel grates for their durability, but as a cook I have always liked the coated cast iron grates better. They may not last *quite* as long, but they hold a lot more heat and are fantastic for searing. On the other hand, the stainless flavorizer bars are a no-brainer choice on a grill you plan to use for a long time, though.