The main problem with Wilkie is probably congress. If Wilkie wants to get anything done in 1941, he's going to have to work either with Republicans who disagree with him, or Democrats who probably aren't going to be thrilled to be working with an ex-Democrat. Also, Wilkie's sheer inexperience would be problematic.
I wonder, is Wilkie a viable candidate in a situation where Roosevelt isn't running? Since that's about the only situation in which a Wilkie Presidency is possible. I know, this is a bit of a tangent since I didn't want to get bogged down into discussions of how a "Landon Presidency" is extremely implausible, I knew that already. Anyway, if FDR decides to be a two termer, does Wilkie still have a chance at the nomination?
If not, the consequences of the 1940 election could be dire. There's a chance we end up with an isolationist District Attorney as President of the United States in the middle of the Second World War. True, he'd be more experienced than Wilkie, but his non interventionist stance would be very problematic.