Rand has been developing a connection with Mat and Perrin as well as Moridin. I have a feeling that all 3 of these connections will play a huge role in the Last Battle.

One interesting parallel going on right now is the order and chaos parallel. Rand has developing mental connections via Moridin-- this represents chaos. Rand has also been developing mental connections with Mat and Perrin-- this represents order. I think the order and chaos parallel is going to be the deciding factor in the Last Battle.

Rand has his own ta'veren effect, but from Min's viewings it is evident that Rand's ta'veren effect alone won't be enough to overcome the Dark One (the whole lights in the darkness viewing). Mat and Perrin are also needed. This is why Moridin has been so focused on cutting one of the legs of the 'tripod.'

This is just a wild guess, but I think that Rand will find a way to combine all three of their ta'veren powers into one. He may do this via the mental connections that have already formed, or possibly via Callandor. From TGS we know that the 'three will become one.' It will be interesting to see who the 'three' are-- it may or may not refer to the three ta'veren.

We also know that Callandor may have a special use that has been undiscovered at this point. It would be really interesting if it had something to do with channeling the ta'veren effect.

'Belief and order bring strength' is what Fel said. The pattern's way of bringing order has been via ta'veren. Therefore I think 'order' will be key to fixing the pattern and locking away the Dark One. Rand has been very dark at this point-- he cannot bring order in pre-Dragonmount mindstate. 'The Dragon is one with the Land.' Rand was very dark and he brought destruction and food rotting with him-- as evidenced by what happened in Arad Doman. Rand will have to come back to the light and truly believe in the key aspects of the light such as love and joy. As Rand's inner-light shines again, his ta'veren effect can once again bring order to the land.

Cadsuane's goal of teaching Rand 'laughter and tears' was probably far more important than she could have possibly realized. Until Rand rediscovered laughter on Dragonmount, there was no possible way for him to bring the order necessary to fix the pattern and defeat the dark one.

Fain will probably play a side role. Rand could find numerous usages of Fain as his energy counters the Dark Ones-- but I don't have any fresh ideas on Fain's role.