Here's a solution to a few of the problems. Make a new section called something like player indexes, which will list all the players and link to the movie collection of each player. Each person who makes speed runs will register with the site, and will get his own page in the player indexes. Each person will be able to edit only his own page, and will be able to upload his new fmvs or delete fmvs from his page, and also will be able to type a discription of each fmv. On the player indexes main page, there will be some kind of calendar where the players announce their new fmvs that they want to be published (though they don't have to announce them). Bisqwit can then look at the calendar and decide which ones to be published. In addition to a player index, there should also be a game index. When a player uploads an fmv to his movie collection, he should also be able to add it (along with the description of the fmv that he typed) to a collection of movies for that game, and also be able to delete only his own movies from the game index. For each game on the nesvideos page, there should be a link to the game's movie collection in the game index.
Now I'll reply to some of the things Bisqwit said:
There's no easy way to know which authors have contributed most or to search by author
The previous paragraph solves this. All you have to do is put a number next to each player in the player index that says how many fmvs are in his movie collection.
More and more movies are going to have various different versions, and there is no single good way to say which movie is the right one to represent the game
Except for a few exceptions, the representative movie should usually be the fastest one (if there's a warp version, a non-warp version, and a tricks version, the non-warp version and the tricks version should just be in the games movie collection in the game index, and also should not be announced on the calendar). In the case when it's hard to say which movie is best, the video displayed on the nesvideos page should be the one with the highest rating (which would be an average of all the ratings people give the movie) among the movies that have been announced on the calendar. Movies in the game index should be sortable by rating, player, or length.
Listing all same-game submissions under the same entry makes the entry long and hard to read
Creating a new entry for each movie of the same game clutters the list
I already solved these two problems.
There's no easy way to download all the new movies since your last visit
You could put links to the fmvs in the latest updates section at the top of the nexvideos page. New movies could be a different color than old movies.
Updates to the site depend too much on one webmaster
Handling of the submissions depend too much on one webmaster
With my new system a lot of the work would be done by the players. All you would have to do is check the calendar for new fmv announcements and encode movies, though maybe other people could volunteer to help encode some of the movies.
There is no mechanism to include long explanations for movies, yet people would be interested in seeing detailed explanations of tricks used
In the game index there could also be links at the bottom of the page to articles that players write about all the details of the movies.
Not all submissions can be accepted - having the top quality is a requirement for the site to stay interesting
The nesvideos page would only have top quality movies, but the game index could have any movie that a player chooses to put in it.
Bandwidth is a very concrete factor for users and for the server - it must not explode.
I thought BitTorrent solved the bandwidth problem.
Turning the site into a Wiki - anyone could edit any content, all changes would be archived so things could be swiftly restored in case a vandal shows up
This is a bad idea because of the emu speed run haters. People should only be able to edit their own movie collection in the player index and their own movies and descriptions of their movies in the game index.
Categories - for different types of movies, for different games
Ok, I suppose you could make genre one of the methods of sorting the movies on the nesvideos page.
Search / grouping facilities: list movies by authors, list movies by games, "show all movies of Castlevania 3"
Being able to sort movies in different ways as well as being able to search in different ways is a good idea. You could show all Castevania 3 movies by opening it's movie collection in the game index.
History: "Show all past versions of Solstice movies"
I don't think this is necessary, though a player could choose to keep all his versions of a movie in the game index if he wants to. However, it might be a better idea for each player to only keep his latest version in the game index and all his versions in the player's movie collection. However, players should not be required to keep all his versions of a movie in his movie collection.
Voting system for various aspects of movies
People being able to rate the movies is a good idea, but I haven't decided yet if they should be able to rate the different aspects of the movies yet, such as speed, surprisingness, and coolness. I'll have to think more about this.
Sort by name
Sort by rank (from voting system)
Sorting by name is a good idea on both the nesvideos page and the game index. However, sorting by rating should not be used on the nesvideos page to compare movies of different games, but it could be a sorting option in the game index.
Public submission queues
I'm not sure what you mean by this.
Edit: Wow, I think that might have been my longest post on a forum ever.