Momentum and Dual Striking can be used simultaneously. Dual Striking needs to be reactivated each time you enter a new zone, even if it seems active, to work properly.
An attack roll for each weapon is performed independently, either weapon or both can hit. Weapon buff spells, such as Flaming Weapons are applied for each weapon. "Miss" will only appear on HUD if both attack rolls fail to hit.
Critical hits are still possible in conjunction with auto-crit skills (attacking out of stealth, Pinpoint Strike, Death Hex). All attack rolls which would normally be critical hits are converted into normal hits. All attack rolls which would normally be normal hits are converted into critical hits.
Before Dual-Weapon Mastery this skill would slow a waraxe (main)/dagger (off) average attack of 1.2 seconds down to the main hand speed of 1.4 seconds resulting in only a 14% net increase in hits. (See Bugs section below) After Dual-Weapon Mastery the two weapons being swapped in hands results in an whopping 60% net increase in hits. Compare this to the fact that +50% critical chance and +50% critical damage combined would only give a total of 50% more base damage with no boost to damage added by Runes, Flaming Weapons, or similar. See Weapons (Origins) and Combat mechanics (Origins) to better understand why this is. This is the superior choice for warriors' damage (rouges can backstab) until Awakening saga when better critical gear becomes available.
One of the three possible animations does not perform attack rolls. As such, 1/3 of attacks will never connect at all. Even with these misses, dual striking still generates 33% more hits than attacking normally. An unofficial fix for PC can be found here.
The off-hand weapon is not taken into account when determining attack speed, only the main-hand. For example, a dagger (main)/longsword (off) setup will attack 40% faster than longsword (main)/dagger (off).