OK, strictly speaking, the problem has more to do with the Earth and the sun not being able to get their shit together and create a year that's composed of a nice round number of days: 365.25 doesn't divide evenly by anything, no matter what the pope says.

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"God's working on changing what integers are, right now."

Still, that hasn't stopped people from trying. And 365.25 is kind of close to 364, which is 28 times 13. That means we could have nice, even 28-day months, except we'll have 13 of them, which is basically the unevenest number there is. And we'd still have a spare day each year, which we'd have to do something with. It probably couldn't be a regular day. These guys who invented a 13-month calendar want to call it the "day out of time." The guys who invented this 13-month calendar call the spare day "Year Day," which sounds less dumb until you think about it, at which point it sounds much, much dumber. And it wasn't even just kooks promoting these alternative calendars. After World War II, the United Nations was seriously considering a "World Calendar" that featured 12 months (phew) but still had those insane "blank days," which are so confusing.

None of these proposals have gone anywhere, although unlike some of the other items on this list, it's not just because people were lazy. No, it turns out that the idea of a blank day is really hard for most religions to wrap their heads around. If you're supposed to dedicate every Sunday to worshiping God and you spend the day after Saturday drinking beer in a park because that's the blank day for the year, is God going to be cool with your accounting?

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"HINT: NO."

To counteract this subtle psychological effect, different projections have been proposed that more accurately portray the relative sizes of the continents. Like this Gall-Peters projection ...

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... which makes the Northern Hemisphere look like it got stepped on.

In the 1970s, the (re-)inventor of the Gall-Peters projection, Arno Peters, began lobbying the map users of the world to use his projection instead of the Mercator for the above reasons. This slightly noble pursuit wasn't helped by the fact that, by most accounts, Peters was a colossal ass about the whole thing. Notably, the argument he was making wasn't new; cartographers had long known and pointed out the problems with the Mercator and advocated the use of more reasonable projections, like the Robinson. Also, the Gall-Peters map isn't "less" distorting than the Mercator; it's just differently distorting. And finally, the reason we call it the Gall-Peters projection is because it was first invented by some dude called Gall a hundred-odd years earlier, which Peters never really acknowledged.

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"I didn't think anyone but me could create something so ugly."

Although a few users switched to the Gall-Peters projection, a lot didn't, and the argument kind of faded away. The only lasting impact the whole debate made was that most people realized that guys who talk about maps are really boring.

The United States does not use the metric system, and instead still uses a system of measures based on the size of various parts of their anatomy. Although most of the world switched to the metric system in the 19th century, the English-speaking world managed to hold off until the 1970s, when they eventually acknowledged the benefits of the metric system and caved in. Only the United States refused.

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All 11 trillion hogshead/feet of it.

Obviously, there are some serious complications in switching your country's system of measurement. All your old signs are now useless. Any data you gathered in the old units have to be converted before they can be reused, which is a big problem for things like engineering or surveying. And all of your old recipes and calculations and empirical formulas have to be redone. Converting to a new system of measurement basically consigns your country to a muddled few years where everyone has to scratch their heads and be capable of converting between the two.

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"I'll have a six-pack, please."
"Sir?"
*sigh* "I'll have 0.6 decabeers, please."

Consequently, when the United States sort of tried to implement the metric system, it did so only on a voluntary basis, with no mandate to force the private sector to use it, which the private sector, taking one look at all the hassle, promptly didn't do. The metric system was adopted in weird sorts of half measures. It's essentially universal in the sciences, but much less so in engineering, and almost nonexistent in construction. In consumer goods, there's an odd mishmash of units, where most items are sold in ounces or hogs or whatever, with a few odd exceptions, like 2-liter bottles of Coke, or 2 grams of coke, or 9 mm ammunition.

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Which could come in handy for either your Coke or your coke-dealing business, I'm not sure which.

It's really the worst of all possible worlds, the metric system having penetrated enough that if you're in any field where you have to measure things, you have to be capable of working with both systems, and if you make any mistakes, oh whoops, you've lost a $125 million spaceship. Instead of a few years of confused conversions, the United States has backed itself into a few decades of confused conversions instead.