You can get a Mighty Blow when you use a channeled skill, but only if you kill enough monsters fast enough. The fact that you use a channeled skill to kill enough monsters does not qualify for Mighty Blow unless you kill them quickly enough.
I'm pretty sure that, in general, Mighty Blow does not care at all on how you got the kills - from a single channeled skill, from an AoE attack, from a combination of mines and 2 different skills - it only cares about 6+ kills in a short enough timespan (about a second). So whether a skill is channeled or not has no impact here.
But either way I was able to 100% verify that Mighty Blow is obtainable from channeled skills, but only when you kill the monsters quickly enough.
According to Bashiok:
...faster speed weapons consume more resource but may do more damage. Channeled skills might still be better with slower weapons though because on a channeled skill, you have as much mobility as you want, so the "mobility" and "overkill" advantages of faster weapons are eroded with channeled abilities, so all you’re left with is increased mana cost for increased damage.
So yes, a faster weapon will cause more skills to tick faster, resulting in you dealing more damage over time, but will result in you using up more resources as you are channeling faster.
Channeling mechanics
Let's use Ray of Frost as an example,
Cost: 20 Arcane Power
Effect: Channel a beam of frost that deals 215% weapon damage as Cold.
Since this is a channeled skill. The resource cost ticks by 10 and drains that much Arcane Power at twice the speed of your weapon. If your attack speed is 1 attack per second, instead of draining 20 Arcane Power once per second, it will drain 10 Arcane Power every half seconds.
Additionally, Since Ray of Frost is a channeled spell. It is broken down into many small attacks that deal a total of 215% weapon damage based on your attack speed. If your attack speed is 1 attack per second, it will deal a total of 215% weapon damage per second.
tl;dr: The faster the weapon attack speed, the faster the drain; slower the weapon attack speed, slower the drain.
Damage-dealing
Assuming two weapons have the same damage, the faster weapon will use up resources faster than the slower one when channeling, but the faster weapon will take less time to do full damage than the slower one.
An axe at 15 damage and 1.0 attack speed will drain slower. (15 DPS)
A wand at 15 damage and 1.5 attack speed will drain faster, but will do
the same damage faster. (22.5 DPS)
Best Answer
Attack speed increases animation time, thus gives you the ability to have more primary animations go off. (Primary animations are always forced to be displayed, secondary animations are only displayed if you are idle, for example the barbarians war cries)
In the case of channeling (a primary animation, that would be interrupted if you cast another primary animation, because only one can be displayed at a time) your damage ticks will occur more frequentlyb tu your resource wil drain faster as well, making very high attackspeed on channeled abilities rather useless. It'd be better to have a slow, hard hitting weapon, since most challens have pretty fast damage ticks already.
Summons benefit from attackspeed in two ways. First your summoning animation is faster, meaning you can drop that Gargantuan in the enemies face quicker, to faster go and collect loot again.
Second, most pets scale proportional to your attack speed, meaning if your attack speed in the Stats-Page is higher, your pets will also hit faster. (Also the Thasker and Theo's Gloves multiply with your attacckspeed, making your pets go berserk)
For Fire/Forget spells, you oughta read up on every spell you want to know about seperatly, because they are all individual. (Frozen orb will be casted faster but the spikes it shoots stay the same rate - Hydra will be casted faster but also attacks faster, etc.)
Finally damage over time spells only benefit from the cast animation (wich might be useful for Jade Harvester builds to get those dots in faster before you blow them up) but do not increase their damage if you run higher attackspeed. (Critchance and Critical hit Damage do increase the damage of dots)
I know this is a very old question, but seeing that the only answer was completely wrong in most points (dunno what's with that) i figured i'd go and set it right.
Hope I was helpful, guy from 3 years ago.
Tophatcrusader