Episode 10 is widely considered the Tear Jerker episode, with everyone sending one last message home (and Kodai doesn't even have anybody), but Dr. Sado drunkenly yelling about the boundless universe to his mostly uninterested cat delivers a much needed Mood Whiplash.
In the second season the Yamato tries to lose the chasing Andromeda by flying through the asteroid belt... Only for the Andromeda to fly around the belt and lazily wait them on the other side. The reactions of the crew are priceless.
One of the redone scenes from the anime gets turned into this. Kodai initially turns down Okita's request to be acting captain at first, whereupon Okita turns on the PA system and turns it into an official announcement.
Sado's spooked reaction at Kodai surviving deadly radiation poisoning.