1. At the time of the Battle of Vulcan, Admiral Archer has been planning to retire next year for twenty-two years. Looking at the remaining rosters, the few surviving ships, the decimation of their training and graduate programs, the lack of qualified personnel to perform even a fraction of the necessary repairs, he knows with absolute surety that he will die at his post, because retirement is suddenly a luxury that Starfleet can no longer afford to offer.
2. He loses one great-grandchild on the USS Farragut, a third-year student named Kayla who'd had a promising engineering career ahead of her. Five more of his descendants sign up to Starfleet in the days following, including her younger brother, along with thousands of others from every member and allied planet. He's never been prouder of every one of them.
3. He was actually pretty pissed about his dog being used as a test subject without his permission. Even if it did re-materialise eventually, it refused to leave the house for months afterwards and reacted badly to broad accents for ever after. He, though, had planned revenge by means of giving Mr Scott the most awkward grad students and underlings for the rest of his career – it was Shran who'd hacked the duty roster and then convinced four other admirals to sign off on the changes.
He'd taken the kidnapping personally, even if he denied everything later, and had had to be prevented from claiming an honour duel. Scotty had no idea how easy he'd got off with just a few months on an awkward duty station.
4. He couldn't help but feel like things were a little too circular when it came to rebuilding the Academy from scratch a hundred years after he'd helped build it in the first place. He dug up his old files, blew the metaphorical dust off them and sent them all to Admiral Pike on a datastick with a covering note saying, 'What not to do.' It wasn't bad for its time, but they'll get it right this time.
5. He's been following Kirk's career with interest, because Chris Pike thinks he's worth watching, and he trained Pike himself. He was the first to sign off on Kirk getting the new Enterprise. If one person's going to be representing the Federation to unknown alien races, it should be one who thrives on chaos and pulls off ridiculously long odds as easy as breathing. The galaxy isn't the same place as it was in his early days, and Kirk is already a master at getting his own way. The right officers will keep him from abusing that innate talent and he's not the only one who pushes for the Vulcan commander. He knows what the start of a very unlikely friendship looks like and he thinks this one will be spectacular if they don't kill each other.
He's been shaping the Federation for most of his life, one way or another, and the way he sees it, this can be his last say in what the future will bring. He won't be around to see it, but he takes a personal interest in hundreds of individuals now, his own blood and Shran's and kin of crew-members past of half a dozen species, and those, like Pike, that he's just picked up along the way and every one of them is his personal responsibility.
He's happy to leave them in Kirk's hands.