Browsing through various websites and forums, people keep pointing out that In first contact, that while the Enterprise is surveying the Romulan Neutral Zone, Starfleet engages the borg at Earth, making it seem like Enterprise gets there in no time.
Well seems like a bad plot hole...but it isnt. THe battle that the Enterprise over hears , is occuring in the TYPHON SECTOR. During the breifing scene we hear Picard say "Admiral Hayes is mobilizing a fleet in the Typhon Sector." Well...if this is the Typhon Sector that has the Typhon Expanse...then the Borg were still pretty far from Earth. Picard would have known that he would need to head to Earth at maximum warp to intercept the borg in time. Also, when the movie cuts to the Borg after the Enterprise Warps...It is just then arriving at Earth. Also one has to consider the Enterprise E has a warp 9.9+ engine.