So if I have the new Secret Invasion Spider-Man equipped with both the Maneuver(he has the boot symbol) and Vault (he has Leap / Climb) feats, is the following situation possible.

I am based with an opponent asn I give Spider-Man an action to use his Flurry that is granted from his Web-Punch Special Power. I make the first attack and successful or not I use Maneuver to position the target on the exact opposite side of Spider-Man. I then use Vault to position Spider-Man exactly opposite the target. Now I make the second attack from the flurry, and so the same series of movements from the feat again (possibly not the Spider-Man depending on who I want where in the end for other lines of fire).

Is this possibleto move the target this far (4 squares), or am I missing something here?

Vault

Prerequisites: Combat Reflexes or Leap/Climb

Choose a character.

After the character resolves a close combat action, it may be placed in any square in which it may legally be placed adjacent to a target of the action at the same elevation as the target.

Spidey won't be able to use Vault until after the entire action (both Flurry attacks) resolves.

You can indeed use Maneuver after each attack (per its description), but Vault will only gain you one square, max (barring things like knockback).

Vault can only be used after the entire action is resolved - so you can only Vault once, after the second attack. You can Maneuver the target after each attack though. After the second attack Maneuver will activate before Vault, BTW.

Boy, it would be nice (and thematic) if Spidey could use his Spider-Speed and Spider-Agility to dance around an opponent, blinding them with punches until they stumble off the edge of the building - but no luck!

Dang. This game is really constricted in what you can do, isn't it?

If you do want to be able to toss your opponent around like a rag doll my suggestion is to outfit Devil Dinosaur and Moon Boy with Sidestep and Maneuver and do a duo attack:
1. Perform first attack against enemy within striking distance.
2. Use Maneuver to reposition said enemy to other side of DD&MB (could mean 4-5 squares with their double base and Giant Reach).
3. Use Sidestep to reposition DD&MB on other side of enemy.
4. Perform second Duo attack against enemy
5. Reposition enemy again.
I'm not sure exactly how far you could move the enemy with this tactic, but it should be 8-10 squares with the proper set up.

That's what I was missing. Thanks for the answers.