In order for this set to work, I need to come up with a comprehensive list of all the things blue accomplishes in a set that need to be there, and then make sure those things are covered by the other colors. I'm going to start by listing the most obvious things, but if you have anything to add that I've missed, even if it's a small things, please tell me. :)
1. "Soft" Counterspell
2. "Hard" Counterspell (will have to be conditional in Anydria)
3. Bounce
4. Card Draw
5. Scrying
6. Mill
7. "Soft" Creature removal
8. Creature snatching
9. Tap/Untap
10. Creature shrinking
11. Looting

Looks good. I made a partial list of abilities seen at common in each colour in the community set (see: http://multiverse.heroku.com/cardsets/162/details_pages/163) I think you have all of the non-creature abilities on the list. There's also a couple of creature abilities, flying, islandwalk and hexproof/shroud, but they already have homes in other colours or aren't necessary for a set to be complete.

I did leave those off, but as you've said, they fit sort of naturally into the other colors already. Looking at your list, I also left of looting, but of course that has a home in Red now.

I assumed "Card filtering" was meant as "looting".

Sorry, I meant things like Ponder. I didn't exactly use the right terminology. :-)

I've heard it called Scrying and Frobbling. In some sets, all colours seem to get a bit of it, as well as artifact. In it's pure form allowing planning ahead, it's probably the bluest thing out there though.

Scrying / frobbling is library manipulation. All colours got scry in Fifth Dawn, but I think that's the only set where red and white got that effect. Although I think Chris is correct in his set Arcunda that all colours could get a mechanic like augury, which he initially nicknamed "scrycling".

Looting / filtering is different from scrying / frobbling / library manipulation: looting / filtering involves actually drawing then discarding cards. Thirst for Knowledge is a classic example of filtering, as is Sift. I think the difference (inasmuch as there is one) between looting and filtering is that looting can never increase the number of cards in your hand, where filtering might or might not.

Looking at http://wiki.mtgsalvation.com/article/Blue, and reviewing Mark Rosewater's article "True Blue", I'd say you've got your bases covered. It also seems important to me to recognize the types of decks that blue has a tendency to run, to understand where the hole in your set are going to pop. Blue likes to play slow stalemate decks that work off the principal that all I need to do is eventually outdraw my opponent in order to win. It also specializes in Mimicry decks full of cards similar to Clone]... decks that copy what the opponent's deck is doing, but doing it better. Third, fish decks specialize in dropping some early threats, then disrupting their opponents game, never quite allowing the opponent's deck to come online and deal with blue's less effecient threats.

When making a world with no blue, I think one needs to look at these three archetypes and decide whether the other 4 colors are intended to fill in the gaps, and create cards that would support this style of play without neccessarily being blue. The alternative would be to take the opposite approach: Assume that these three deck archetypes do not exist, and plan your set around the lack of them.

Why are there 10 blue cards listed this set?

Because this is a holding set for the block, not just the first set.