The main problem stemmed from a few things, mostly his lack of trust in Logaine and his unfounded trust of Taim. Both stem from the fact that he hadn't fully accepted his role and integrated with LTT, and as a result the two "sides" of Rand were at odds with each other.

Rand knows the BT is something that must be dealt with, but he has been putting it off--not a good decision IMO, since the longer he waits, the harder it will be. He has no idea how much difficulty it will be. We know Taim is Forsaken-level strength in the OP, he's obviously had AoL training, and he has a horde of black channelers to boot.

Personally, I think Logaine is Egwene's counterpart to the White Tower, and, working with Nynaeve (who, remember, has recently discovered how to tear the claws of the shadow from mens' minds), will defeat Taim and reunite the BT. Hopefully, this will happen at a critical moment before the WT falls to the Seanchan.