Apple's servers were completely overloaded today by people trying to pre-order the iPhone 4. Users trying to place their pre-orders were routinely hit with "Failed to open page" and "Server failed to respond" errors today.
While some will just wait and try again late tonight or tomorrow, there is some risk of the first day pre-orders selling out. You were able to pre-order the iPad for first day pickup for a few days, but the demand for the iPhone 4 is expected to be much greater. So it is possible that the iPhone 4 could sell-out much earlier. The real exasperating part is that if the process fails, you have to start back from the very start of the ordering process. Why can't they just remember your choices and allow you to continue?
Our best suggestion, just keep trying!
Let us know in the comments if you were able to pre-order your iPhone 4. I'll keep trying, and hopefully I will get my iPhone 4 pre-ordered before they sell out.
Update: I was just able to complete a pre-order, on my first try, using Apple's new Apple Store app. I suggest you give that a try. It's only 1.6 MB, so should be downloadable by everyone over Edge/3G.