Education.
Delete non useful (history, astronomy) Insert useful (logic, ethics, mnemonics(not great but better than history)) If the world has changed over 100 years, but the learning about it hasn't, you're doing it wrong.

Congressional Secret Ballot.
Perverse incentives. Congress used to be able to vote privately, now when a corporation buys your vote as a congressmen, they can verify you deliver what they paid for. "Cardboard box reform"

Better candidate pool
Geniuses don't go into politics, the pay sucks and you can't get much done. We can at least fix the pay. If bad voting, but good candidate pool then still win. If great voting but bad pool, only lose. What use is voting when you have choice of puppet A or puppet B both presented by the same megacorps?

Better voting by better voters.
Voting licenses. If you are stupid enough that I don't want you editing the settings of my OS on my computer, why would I want you editing my democracy? Is not governance advanced enough and complicated enough to require a license to effect changes through voting, just as cutting hair is licensed? Yes, its dangerous, yes if the tests suck you get unfair amplified power to the test makers. However, if you want greatness, you must select for it. You will never having voting excellence if you don't try.

Better voting by better intel gathering.
Why capture a single data point of "who do you want to win?" Choose instead "put these people in order you'd take them." Now you've captured 8x the data from the voter? Now you can combined the ordered lists to get an electorate that everyone kind of likes and few people hate, as opposed to the 51 percent voting to gouge out the eyes of the 49 for idle pleasure. https://en.wikipedia.org/wiki/Condorcet_method

Isolate government from currency.
Peer to peer value transfer. A proper BTC/zerocoin might work here. Artificially low interest rates amply mis and mal-investment causing boom and bust cycles that harm the human psycological ratcheting effect. We prefer slow and always better to fast up and fast down pain.

Cooperation.
More perverse incentives. Why must we all keep our greatest ideas secret, so that no one else runs with and executes to our detriment? If you could make a lower barrier to entry profitable collaboration, or set a standard by which idea givers were commonly rewarded, people may be less secretive. This isn't just a corporate problem, this is a science problem as well. Publish or perish? Well better keep those good research ideas to yourself. How many websites have you been on that desperately needed improvement, yet you kept your ideas a secret?

Science is broken
If half the papers published produce results that can't be replicated, then lots of scientists are fucking up. At least remove the "HARKing" Hypothesizing after the results are known. Publish more of what hasn't worked and isn't interesting to save others from unknowingly going down the same dead ends. Sadly, if the science is so bad as to be unreplicable, then who cares if you publish or not as you were 50/50 wrong anyway… The math could be better, however the idea stands that bad science can and is being done to the detriment of the world. Thinking you know a thing and being wrong about it, is worse than thinking you do not know a thing and being accurate in your estimation.

Undercrowding
Progress comes from humans. Through enough shit at the wall, more of it sticks. We need more humans, preferably the useful kind.

Spreading great ideas
The mormans got a bible in every hotel room, what better book could be equally funded and distributed?

Luckily this can be quite a long list as the world is ripe for improvement.