Daniels says that he can get Archer back to Enterprise because he has the spatial coordinates. However, Enterprise was moved to the Suliban Helix since they left, therefore it wouldn't be at the same spatial coordinates.

In the future Daniels and Archer see a devastated Earth as the timeline has been radically changed, yet Daniels' apartment is still recognizable (indeed the apartment building is still standing) and the library is still in the same place.

The library that Daniels and Archer visit in the future only seems to have standard paper books. Even libraries today have digital media and computers. Of course none of the computer equipment would work, but it should still be there.

Not only do a number of official sources say that phasers and phase cannons can't be fired at warp (such as Roddenberry's Writers' Bible for Next Generation, but in "Fallen Hero" Reed says they can't fire phase cannons at warp speed without blowing out the warp nacelles. And yet here they do it just fine. In TOS they fire phasers at warp, and in "Fallen Hero", Reed's comment can be dismissed because maybe the canons were upgraded, or maybe he wasn't as familar with the ship design as Trip. Yet when Reed says that the phase cannons cannot be fired at warp, he also says that he has been working on the problem. Reed has a prodigious history with regards to research; in "Vox Sola", he (a tactical officer with no detailed background in scientific research) creates an impromptu force field and, in later episodes, makes modifications to weaponry with astounding results. Considering this history, attributing the solution of the phase-cannon-at-warp thing to Reed doesn't seem far-fetched.

It seems the writer's handbook is off (as we expect later publications to correspond with the rules set by previous publications and not vice versa).