Rand's POV says the amount of the Powers he was holding would soon burn him away.  The sword was flawed so there was no buffer preventing him from drawing too much of the power.   Plus there were other ways to burn yourself out, channeling while exhausted for instance.

Yes, but Moridin was using Calandor at the time, not Rand.  Also, Rand was in a link with two women.  It wouldn't matter that there was no buffer on the sword because he was protected by the two women.  That is why Cadsuane said the only safe way to use the sword was in a link with two women.  That is absolutely what Rand was thinking at the time, but since Moirane and Nynaeve suffered no ill effects, the same should be true for Rand.  Makes no difference in the end, as Rand's body ended up dead, and Rand (in Moridin) unable to channel.  I just read that scene I referenced before between Demandred and Taim as Brandon's attempt, though a bit heavy handed, to set up post TG Rand being unable to channel.

Interesting theory but it has a flaw. The (in)ability to channel comes from the soul, not the body. Cyande stated this and when Nynaeve healed Logain she said the his body had no wounds (and that should mean that the wound from his servering was on the soul, I guess).

So Moridin's severing should have been swapped with his soul.

Again, true, but I believe the body plays a role as well.  That is why when the forsaken were getting reborn (Moridin, Cyndane, the 'Gars, etc...) not just any body would do.  I really don't know if Moridin would have been able to channel in Rand's body, post swap (assuming he'd been conscious).  I believe that there was an RJ quote at some point that said that a soul with the ability to channel didn't end up able to channel every time they are reborn.

As I said in my first post, it is splitting hairs, because it is clear that Rand can't channel post swap.  He is also, unquestionably as unique case.  If anyone would be able to just get over being severed, it would be Rand... 

It might be splitting hairs, but I always assumed that Rand didn't experience any of the side effects of severing/burning out because his body wasn't severed/burned out, Moridin's was.  Demandred says earlier in AMoL that drawing the True Power through someone else (like he did to Taim and Rand and the ladies did to Moridin) was a good way to burn someone out.  Rand was protected from overdrawing by being in the link with two women.  Moridin was burned out during the sealing and then Rand body swapped into his body, which had already lost the ability to channel. Perhaps it is the act of being severed/burned out that causes the side effects.

 

I didn't mean Gaul was not an exceptional fighter, I meant not for an Aiel. Never is he hailed as being one of the Aiel's great heroes, it seems he's just the run of the mill Aiel (which means he's roughly as good as the 5 or 10 best fighters in the entire wetlands). My point was that all the Aiel seem able to do things like that, it just isnt a big deal.

 

Quite the opposite.  We are told that Gaul is basically next in line to be sent to Rhuidian to become Clan Chief.  I would say this puts him pretty high up on the list of exceptional fighters. 

The fact is, Aiel would not be decimated by a heavy cavalry charge, because, they would never put themselves in a position where a heavy cavalry would have the opportunity to charge.  The Aiel are very difficult to surprise.  If they were engaging an enemy who were using heavy cavalry, they would make sure that the charge were not an option before they engaged. 

He is enough older than Rand, thus he is definitly out of sparker range.  Rand started channeling at about 18, Galad is several years older.  He would have sparked several years prior to the events in The Eye of the World.

There is one problem with Galad channeling.  He we would have to be a sparker, as, clearly no one has trained him while he was serving in the CotL.  If he were a sparker, he would have actually channeled by now, not to mention the channeling sickness (like the sickness Rand experienced in TEotW).  Remember when Rand was figuring out how to channel, he cured Bella and blew up an Inn.  Galad has done nothing like this.  In fact all he has done is shown that he is an intelligent, exceptional swordsman, which, we already knew he was.  We have had enough POV's of his and chapters about him that any channeling or debilitating channeling sickness would be noted.  It is possible that he can be taught, but he isn't a sparker, and he certainly wasn't embracing Saidin when he fought Valda. 

That knowledge should have let Moiraine know that he was the soldier who found the prophacy baby on the mountain.

 

Only, there was no soldier in the prophecy. The prophecy was essentially that the Dragon would be born on Dragonmount to a maiden. No mention of an Aiel, no mention of a soldier.

 

You're right there was no soldier mentioned in the prophacies, BUT Moiraine later explained to Rand that stories of a soldier who found a baby on the mountain led her to the TR. That soldier obviously being Tam. I just thought of this, but just knowing that Tam had been 'out and about' when the other boy's father's hadn't should have been enough to alert Moiraine to the One.

That soldier being Tam is obvious to us, as we have read the books, but would it be so to Moiraine?  I am not so sure.  So far as Moirane was told, all three boys were born in the TR.  The fact that Nyneve lied to Moiraine's face about where Rand was born suggest that no one else in the TR was likely to be any more forthcomming.  Remember also, from an outsider's perspective, Matt's father could have been just as likely to be said mysterious soldier.  After all, either Tam or Able Cauthon always win the archery and staff competitions at fair days.  Frankly, if the father's of two of the boys born within the necessary time frame could possibly be the soldier she had followed, it isn't too far a strech to assume that maybe the third father could be too, even if she couldn't find any direct evidence.  Remember how stubborn TR folk are known to be.  If a stranger, a clearly rich stranger with a heavily armed escort just showed up and started asking questions about town folk, I doubt seriously that they would be all that forthcomming.  Given more time, could she have figured out who the soldier was, and thus who the Dragon reborn was?  Absolutely.  The trolloc attack didn't give her enough time.  It has been too long since I reread, but how long was Moirane actually in Emmonds Feild before the Trollocs attacked? Two days?  No where near enought time to get any reliable information.  Finally, as it was stated previously.  The attacks were clearly aimed at all three.  What the DO wants Moirane was going to oppose.