I think you can forgive the early writers a bit more since the warp factor system wasn't really well defined back then. Also, many people have hypothesised that the edge of the galaxy could be crossing the width of the disc rather than the far edge - still a huge distance but not as huge.
The problem I have is that the plot of the new movie doesn't work if you apply existing rules to it. Vulcan stations and scanners would have known that the Narada was on course for it days or at least hours before it arrived (or did it have a cloak - I don't recall that). Enterprise could probably crank a bit more speed out temporarily to catch up with the fleet over a longer journey and would most likely have arrived in plenty of time and would probably have had time to intercept the Narada before reaching Vulcan etc. The current plot makes the Federation look a bit more incompetent than normal. Maybe Kirk really is Captain ++ material after one day on the job by their standards.
but it isnt just the early writers.
look as others have said the writers never let some technical issues get in the way of a what they considered to be a good story.
and in the early days fans understood this and thus was born the fun of trying to find interesting explanations for why things were the way they were.
as for narada having a cloak ;it is very possible in the years waiting for spock and preparing to break nero free the crew worked on upgraded for the ship.
they could have had specs for some of the earlier cloaking devices which even a two version earlier cloak would be very advanced for the movie time period.for all we know some of the narada crew could have been former military.
and yes to answer some one else reaching maxium warp might take awhile.
while a ship can go to warp near a planet (numerous examples through trek) they might not be able to get to maxium warp till away from a planetary system.
and if they needed to travel and get into a corridor this might mean slowing down or even dropping out of warp while going into the corridor and then going to maxium warp.
we know it took some time because bones and others had time to change uniforms.
actually maxium warp for a corridor might be different then maxium warp elsewhere.
especially if this was corridor that for some reason might only be used for extreme emergencies.
it would also help to explain why they were sensor blind until they got to vulcan if they were traveling in some type of warp highway or corridor.
and i dont think either enterprise or the narada took it back to earth.
that seemed to take longer then the trip to vulcan.
it may be the corridor was afected in some way when vulcan exploded.