Corrected entry: At the beginning of the episode, the "Friendship 1" probe does a flyby. On it, you see Federation and Starfleet markings. During the briefing after the credits, Tuvok states that the probe was launched 4 years after Zephram Cochrane's first warp flight. Cochrane's warp flight was in 2063 and the probe was launched in 2067 The United Federation of Planets didn't exist until 2161, and even though there was techinically a Starfleet, it's well known that it didn't adopt the "arrowhead" (aka "Delta) style symbol until the 2240's.
poehitman
22nd Jul 2010
Correction: Fan speculation and trivia generated in other media (novels, comics, blueprints, guides, etc) cannot be used to gauge a mistake. Mistakes only count if they contradict what was established in a previous film or television episode. And the date of origin of the arrowhead insignia has never been stated in any.
JC Fernandez