A lot more can go wrong with a community of billions of humans than with an isolated starship with frozen embryos traveling the void between the stars, very little is likely to happen during that almost 5000 year dormant cruise.
Ahem. You're saying that on a Trek board.
1) The ship could be struck by a piece of interstellar debris
2) The AI could get bored and start playing with the stored DNA, combining it with spider DNA to create mutant monsters.
3) The ship could be colonized by space spiders, who mate with the mutant human/spider people
4) The ship could be boarded by a Ferengi raiding party, who get eaten by the hybrid spiders
3187) The ship could travel through a wormhole and end up back at Earth, dumping human-Ferengi-Romulan-Horta mutant space spiders with Borg implants and telekinetic power back on Earth.
But we're talking real world starship not Star Trek. The most likely thing to happen is getting struck by space debris, and with thick shielding and a relative velocity of 300 km/sec, the ship will likely survive and repair the damage. The Ai basically goes to sleep, so it won't get board, that is the thing about computers, is they can turn themselves off and a timer can wake them again, they don't have to experience time second by second like we do. The ship will be traveling forward in time about as much as it travels in space, getting across those 5000 years of time will be its main purpose, Alpha Centauri is just a destination to separate themselves from the rest of humanity and whatever may go wrong there.