Just a very quick glance, I'm not 100% into the details of the rotation of a retri paladin, but I know how to glance at important stuff:
He died. Before he died he wasn't even the lowest DPS, a frost DK with higher ilvl was being outdpsed by him (which really shouldn't happen). Add to that, he only used Divine Protection 4 times (with a 30 second CD), he didn't bubble when he was dying, and he didn't use FoL to save himself. These are all small things that can end up saving his life that he just doesn't do.
He still had a charge of wings when he died. He used his last charge at around 4min09, so he had at the very least one charge left. You guys even popped hero and he just didn't use it.
He only used Execution Sentence on pull, and at no other point.
I don't know what he was doing between 3:00 and 4:30, but he only used FV once or twice during that timeframe, which is just a bit weird. Maybe he was just Divine Storming? If he was, that's a no-no, should always weave in FV's, even during AoE.
He should use his second pot during the last phase, since this is where the DPS is most critical. More DPS in the other phases is okay, but it doesn't help you nearly as much as having the second pot during hero, cooldowns, and the last phase.
Managed to find a bit more details than I was expecting, hope it was a bit helpful