Well, realistically, we'll have 15 attempts on the hard modes, since they won't be available until after Arthas is available.

It essentially works out to:
Normal: Saurfang available (Phase 1)
Normal: Plagueworks available (Phase 2): 5 attempts to kill Putress
Normal: Crimson Hall available (Phase 3): 10 attempts to kill Putress & Lana'thel
Normal: Frostwing Halls available (Phase 4): 15 attempts to kill Putress, Lana'thel, Sindragosa & Arthas
If Arthas dies, Heroic is available: 15 attempts to kill Putress, Lana'thel and Sindragosa & Arthas*

*The main thing that needs to be clarified is if it is 15 attempts total across both Normal and Heroic or if it 15 attempts in each difficulty.

In 3.3 you can switch a Raid Instance to Heroic Mode while you are inside, so you wouldn't be able to go after Heroic Modes until the next week.

But what he says is still true, unless it's already 16, 20 or whatever after the reset. That part is not yet known, except "it will go up during weeks/months".

I was under the impression that if you killed a boss in normal mode, you would not be able to kill its heroic counterpart.

Right, but I was referring to a situation where you wipe say 3 times on Heroic Putress, 3 times on Heroic Lana'thel, 3 times on Heroic Sindragosa and then wipe 4 times on Heroic Arthas. If you choose to switch it to Normal at that point, would you have a full 15 attempts or would it still be only the 2 attempts left over from Heroic.

The counter is most likely instance wide, changing the difficulty will probably not affect it. The way I understand it is you get a counter at the top of your screen just like in ToGC and it increases once you successfully kill one of the specified bosses.

This is very much like the Zul'Aman timer, that increased by a specific amount when killing bear boss (+15min) or eagle boss(+10min).

Disclaimer: just a guess.

I don't think the number increases after you kill a boss. It is simply 5 attempts total when the first 'final' boss is available, 10 with 2 final bosses, 15 with all of them and then whatever number it might increase to in the following weeks. This number will always be your total number of attempts for those end-of-wing bosses during that raid week.

The gating system seems decent overall, they can't really get around doing something like this anymore. It's also good to see that they got rid of any kind of reward for x attempts left, that was really frustrating sometimes and generally discourages getting new people into the raid for those fights. 5 attempts per phase seems really low though, especially for the normal modes. Actually I don't think there should be any kind of limitation for the normal modes unless there is some kind of technical limitation if they want this implemented for heroic mode. I think a limit on the normal modes could be really bad and frustrating for more casual guilds. As someone else already said, it will lead to alt raids for the more hardcore guilds again.

The only other thing that I don't like about this system is that a lot of the heroic modes will be unlocked during the same week with no limitation at all. This will once again give an advantage to those guilds that raid more, which I believe was the reason why this whole attempt limitation was done in the first place.

The plus side of this system is that you're back to the Ulduar way of having some choice in which heroic mode to attempt. In ToGC, you can't exactly do Normal Beasts and then Heroic Jarraxus like you can do Normal Flame Leviathan and Hard-Mode XT-002.

And I suspect that (once everything is unlocked) you'll have less issue scheduling hard-modes within a week. If you want to do a non-end-boss Heroic mode, you can clear the Wings on normal that you don't want to try on Heroic, and then all that's left in the instance is your Heroic target, its end-boss, and Arthas. For instance, you can full-clear the instance except for Blood Prince Council, Lana'thel, and Arthas, then take shots at Blood Prince Council for a while. When you down them, you have 12-ish tries on Lana'thel Heroic before you either down her or just do her and Arthas on Normal mode. You can do the same thing for Dreamwalker, Festergut, and Rotface. And when attempting Heroic end-boss, you can clear everything else except Arthas, and then swap to Normal mode with 2 attempts left if you fail to down. This beats the heck out of having to quit Heartbreaker to race to Yogg.

Someone on the official forums made an excellent point regarding limited attempts with regard to the creation of Shadowmourne. Each of the three quests for it involves a presumably DPS character taking hits meant for tanks - or at least it does for two of them, I'm not certain what the Putricide quest involves but I assume it's not done in the normal course of the fight. What happens if your potential Shadowmourner dies? Do you wipe it and lose your week's attempt? Or do you continue and postpone Shadowmourne another week? These seem like questions likely to cause serious internal drama.

It's not as if the classes eligible for Shadowmourne (DK, warrior, Paladin) have no choice to become hard targets (either by gearing for the try appropriately or/and taking the right talents/cooldowns). It is a legendary quest after all. Beats the droppable legendaries (glaives, Thori'dal) any time.

3000 attempts was indeed a placeholder counter that showed up on the PTR a few times during testing.