An incomplete and growing list of mistakes that I'd fix if I had a time machine:
Make all languages be written vertically, and stack their lines left-to-right. Everyone being on one writing direction is A+, and vertical writing gives more time for the ink to dry before your hand has to touch it when you're left-handed.
Figure out a universal script that everyone can use. Doesn't have to be too complicated; tons of languages with different sounds use the Latin alphabet fine. I'm kinda in love with the Korean script, tho - it's alphabetic, but is written like it's ideographic, with the letters arranged into syllable-blocks in a standard way. Something like that would be good.
Putting everyone on a single language would be good too, but probably really hard to maintain. Just making sure everyone's writing in a mutually intelligible way is a good start.
Switch everyone to base 6 counting. It's got some great reasons behind it!
- Each of your hands is a single base-6 digit (can represent the values 0-5), so you could count to 35 instead of just 10.
- It's got good divisibility - /2 and /3 (and /6 of course) are just "check the last digit", /4 and /9 are "check the last two digits", /5 is "sum the digits and check if they're /5" (same as /9 in base 10), /7 is "alternately add/subtract the digits and check if they're /7" (same as /11 in base 10).
- The multiplication table is really trivial, almost insultingly so. Similar to the divisibility, multiplying by 2 and 3 are now super easy (like multiplying by 2 and 5 are in base 10).
* | 1| 2| 3| 4| 5| 10| ---------------------- 1| 1| 2| 3| 4| 5| 10| 2| 2| 4|10|12|14| 20| 3| 3|10|13|20|23| 30| 4| 4|12|20|24|32| 40| 5| 5|14|23|32|41| 50| 10|10|20|30|40|50|100|
Numbers in base 6 are about 50% longer than in base 10, which isn't a huge loss. We can compensate for it by making sure the names for the digits are single-syllable, as that boosts your ability to remember strings of digits. Grouping digits into sets of 3 would also feel more "natural" - we might even be able to go up to sets of 6 instead.
I guess when talking about computers, we'd generally use octal (like we use hexadecimal in base 10) - 012345TE. Octal is a lot easier to learn than hex, too.
The Gregorian calendar is stupid. We can't control the length of a day or year, so we can't do anything perfect, but we can at least improve the situation by switching to a consistent 30-day month, with 6 5-day weeks. 12 of these months leaves us with a single 5-day week left over at the end, which should be treated as intercalary and placed at the end. Leap days also go at the end. This makes days consistent across months and years (the 2nd of every month is always the same day of the week, etc), and gives us much easier math in general, in both base 10 and base 6. In base 6, we have 20 months, each containing 10 5-day weeks, or 50 days total. 👌
Keeping time is... fine. It's not great; our time system is clearly based on the dozenal roots in some of our old numbering systems (a day is two dozen hours, an hour is 5 dozen minutes, a minute is 5 dozen seconds), but we can still do better.
We're lucky in that, unlike calendars stuck with the unchangeable physical constants of "day" and "year" (and their terrible ratios), time-keeping is only beholden to the day - the rest of the units are human-made, and can be adjusted as we see fit. So we can switch to proper metric time! In base 10, I prefer dividing the day into 100 "hours", each equivalent to about about 15 of our old minutes, and then further subdividing into 100 "seconds", each very close to our old seconds. 15-minute chunks are very tractable, I feel - we often informally divide the hour into quarter-hours already, because it's a convenient length of time, neither too short to get anything done nor too long to keep track of.
In base 6 I'd do similar, but you can fit in three divisions - 100 hours (each about 40 of our old minutes), split into 100 minutes (each about equal to our old minute), split into 100 seconds (each about 2 of our old seconds).
Time zones, on the other hand, can get fucked. We don't have "season zones" for dates - when it's March 1st, it's March 1st everywhere in the world, regardless of whether that means it's snowy or cool or starting to warm up. Instead we have much fuzzier "seasons" to correspond to the weather, and those do fluctuate based on where you are.
Time should work the same. We should have a single consistent global time, and then pair it with a set of fuzzier "moments" that describe roughly what the light-level/meal time is. Then it's easy to describe when a meeting will happen (at hour 34, or something), but also tell people it's too early (it's still dawn over here at that time), same as we can tell people when we'll vacation (January) and what it'll be like (middle of summer, because we're doing a beach vacation in New Zealand).