As a kid collecting stamps, it was the stamps from Burundi that amazed me most for their color and imagery. What a contrast with these typewriter stamps!
One thing pointed out in the episode is how charging one fixed price really binds the nation together, whether or not you are mailing something to an address around the corner or from NYC to San Francisco (or to more remote regions like the bottom of the Grand Canyon).
This got me thinking: How far can you send an envelope with just one (domestic) stamp? Well it turns out that you can mail a stamp to a military base (say, in Japan) or consulate for the same price as a domestic delivery. But this is routed through the military / consular mail systems and feels a bit like cheating :)
It turns out the tiny island of Palau has a US zip code (96940 - I believe it is now an independent nation? weird). So unless there is a zip code further east than Maine, I guess that's the longest distance you can send a letter entirely through the USPS with one domestic stamp. - about 8,500 miles.
If that's the case, then I think we can do a bit better in the UK, as I believe you can send a letter from Unst (Shetlands) to the British Antarctic Territory, which is over 10,000 miles.
Though, if there's a US station in Antarctica that has a zip code, I'd imagine you could do better by sending from Alaska?