1) The narrator seems to say the mechanics of performing a range vote take nearly the same effort as caveman voting. But, I don't think I saw any suggestions on how to handle this with paper or mail-in ballots. Poking chads seems like it would be MUCH more complicated for a range.
This partially depends on how many scoring levels you allow. The example uses 100, but you could do it with 10, or 3, or just 2 (which is approval voting). Obviously, with 100, it'll be a little tricky to translate that between a paper format and a machine-readable format. But smaller scales would be quite easy.
2) One example he gave (in video 3) was 100/100/0 would win, in the current system, over 90/90/90. I didn't see why. 100/100/0 would translate to 2 votes, while 90/90/90 would translate to 3.
Haven't seen the videos (writing from work, so I haven't seen them) but having seen similar, I have a guess here: It's clearer if you look at it from the perspective of the three voters, rather than the two candidates. Voter1's true opinion is 100/90, as is voter2's, while voter3's is 0/90. So, in a plurality election, voter1 and voter 2 will vote for the first candidate (100 rather than 90), while voter3 votes for the 2nd (90 rather than 0). So the 1st candidate wins. But, if they used score voting (and voted honestly) then the 1st candidate gets 200 points (100+100+0), while the 2nd gets 270 (90+90+90).
3) I wasn't clear whether he was suggesting range voting be used in primaries, or be used to do away with primaries and just use them directly for general elections. I think politically it would be hard to do away with primaries (since it would cause some segment to feel they are losing power), but if used in primaries, I don't think they would then be useful in the general election (since all the range "goodness" was already injected at the primary level, if that makes sense). Still, that would allow local areas to implement their own method of primaries, so maybe some could try range and see how it goes.
Consider this: the only purpose of political parties is to hold primaries.
Primaries are important, because if two similar candidates run in the same election, they will compete, zero-sum, for the same voters.
But, with range voting, since each voter can score each candidate independently, there isn't a zero-sum competition.
On the one hand, this means you could theoretically skip the primaries entirely and throw everyone into a range election. In practice, there is some direct competition when voters begin to act strategically on their ballots, and it gets hard to keep track of very large numbers of candidates, so it's not a bad idea to continue to use primaries, which means parties are still useful things to have.
Finally, even if range voting were used in primaries, as long as more than two parties put forward candidates for the general election, then it is STILL advantageous to use range voting in that general election. It doesn't ALL get baked in.
4) It is the cynic in me, but I am guessing, while the math sounds promising, I expect once power and money is mixed into range voting, it would make it equal to the current method.
Range would deliver better results. It makes it much easier for 3rd parties to grow and eventually compete, and it is more likely to select compromise candidates rather than partisans. The challenge is overcoming the money and power to get there, and fighting the money and power to keep it.
In the 1910s, an alternative voting method called Bucklin was popular. But when it elected someone outside the two major parties, a Socialist no less, the major parties fought hard to eliminate it, and did so successfully.