And ignite+LB is fairly low on damage relative to fireball, so it seems like he didn't spread hit dots often/at all. That could either be a good or bad thing, tbh. Either he felt like killing focus targets a little faster was worth it (and it can be, since the fight gets ridiculously easy to heal after a while). Then again, he did abysmally low damage to the whelps for a fight mage, so perhaps he could use some multi-target fight practice.
His Living Bomb uptime is very low in a lot of those fights. Anything below 80% is pretty bad, and I'm being generous. Not coming first on omnotron as a mage is embarassing unless your shaman are douchenozzles and like to purge omgloldps buffs like mine did on jaraxxus.
It seems like he just needs to focus a bit more on solidifying his rotation, perhaps getting better at positioning and maintaining high uptime while moving as such. A good player avoids fire, a great player does high dps while he avoids it.
I just dont feel like going that detailed into the log analysis, but if he stays out of bad shit you're in good shape. That's the hard part to fix in a player. Honestly, you should just send him to these forums and tell him to read the stickies or some of the better discussion threads we've had about mechanics/rotations and whatnot. Learning a rotation is easy, maybe he just hasn't done much research.
edit- He scorches for what seems to be no reason on cho'gall, but it's possible he runs oom before P3 so he needs the mana (I've had that problem in some 10 man pugs). Also, he uses fireblast on both cho and the adherent which is bad. Fireblast isn't a dps spell. It's for spreading dots and occasionally the stun (like for breaking worshipping). Other than that, LB uptime LB uptime LB uptime!