When Jerry is in the hotel room about to give God a quiz, The Dick Van Dyke Show (1961), is playing on the TV. Carl Reiner - the director of this movie - created and acted in "The Dick Van Dyke Show".
When God makes it rain in Jerry's car, shots taken from Jerry's left show his hair dry, but shots taken from his right show his hair soaking wet. These shots alternate several times, always with the same inconsistency.
When Jerry tries to pick up Adam at school and Adam declines the ride, Jerry opens the car door and the window is open, but a few inches from being fully lowered (there are 3-4 inches of window visible). When Adam closes the door and talks to Jerry through the window, the window is all the way down - and as it is a manual window it could not have been lowered by Jerry in less than a second from the drivers' seat.
The second time John Denver meets the religious reporter from the LA Times, the reporter has a pencil in his mouth. In the next scene, it disappears without it being removed by the reporter.
God: I know how hard it is in these times to have faith. But maybe if you could have the faith to start with, maybe the times would change. You could change them. Think about it. Try. And try not to hurt each other. There's been enough of that. It really gets in the way. I'm a God of very few words and Jerry's already given you mine. However hopeless, helpless, mixed up and scary it all gets, it can work. If you find it hard to believe in me, maybe it would help you to know that I believe in you.
God: "Did Man fall from grace in the Garden of Eden?" I'll tell you something never came out. I made Adam 17. Eve was 15, 16 tops. I figured then 16, 17 was middle age, you know. Who knew people would live so long? Trees I figured had the best chance. Now I realize that they were kids, babies. Young people can't fall from my grace. They're my best things.