I've been leveling my shaman this week and as I was meleeing mobs I was struck by something that a poster mentioned last week about their weapons not being in sync, which was immediately disputed by other posters. I noted that some of my swings were not in sync despite using two identical weapons, first using the Thrallmar honored axes then two Axe of the Legion. I did some observation over an hour or so while power grinding, and my theory is this:

When engaging a target in melee range, the offhand starts with half of its speed in cooldown.

I was able to consistently cause my weapons to strike at the same time when right-clicking or starting autoattack out of melee range then running up to the mob. When I would engage a mob already in melee range, my swings would become out of sync. I didn't really notice it with the Thrallmar axes since they are quite fast, but the extra half second on the Axe of the Legion's delay (2.4 speed) made this more pronounced. I don't currently have any timestamp mods installed, but it seemed that the pattern of hits when starting in melee range was very regular.

This results in two different series of hits depending on what you do. For the purposes of this, Engage means to start melee combat with either a special ability or a special attack* and the timers are multiples of your weapon speed.
Engage at range (with sufficient time for a half-swing):
0: MH-OH
1: MH-OH
2: MH-OH
etc.

Engage in melee range:
0.0:MH
0.5: OH
1.0: MH
1.5: OH
2.0: MH
2.5 OH
etc.

I would guess that this also applies to weapons that aren't matched, but I haven't tested it. Obviously the major ramifications of this are for Flurry and for dual wield classes in PVP. The Flurry bug where you get 4 charges out of a proc by having identical speed weapons is obviously not going to work unless you get your swings in sync. In PVP a rogue who used identical speed weapons that opened with a special attack has his offhand delayed ever so slightly, where a shaman that autoattacks at range will hit with both weapons immediately. There isn't much of a difference there but it might be important in close fights. If there are other people who want to take a look at this and post some findings, I'm sure that this would be an interesting hiccup in meleeing.

*I have not tested if a dual-swing attack like Stormstrike or Mutilate causes this behavior to be bypassed.

Oh, I thought this was known. I found the same thing when I was scoping out gear for my shaman leveling, before I switched to druid. If I recall, standing in melee range and opening with stormstrike will result in staggered swings.