Derpy Hooves, the fan-favorite pegasus with crazy eyes, can be seen several times: watching from a cloud between 5:25 and 07:18, holding the banner at 07:36 and in the crowd at 09:12 and 09:21.
Rainbow Dash asks Twilight if she learned to run reading the "Egghead's guide to running", an apparent play on the title of Douglas Adams' The Hitchhiker's Guide to the Galaxy. Twilight's running is 42, the mystic number from the Guide.
This is the first episode (and the only Season 1 episode) where Rarity doesn't have a single line of dialogue. Though to be fair, she only cameoed in this episode.
The title is a pun on the term "fair-weather friends", which are friends who stop being friends in terms of difficulty.
Friendship Report: Both Applejack and Rainbow learned to be good sports and that friendship can outweigh any competition.