Revealing mistake: When the Federation fleet is preparing to warp to Vulcan, you'll see the first ship blast off, but the second ship blasts off out of nowhere. You could argue that the ship was out of sight and below the Enterprise, but the light trail isn't that long. The light trail starts in front of the Enterprise where you should be able to see a star-ship. (00:40:45)
Revealing mistake: At the end of the film, when Kirk is receiving his medal, in the background you can see the female alien crewmember from the Enterprise bridge clapping with very human-like hands. (01:56:15)
Answer: There's certainly no evidence that they're still within the solar system; the Enterprise arrives dropping out of warp, which would seem to be good evidence that they're not anywhere near Saturn any more. While no specifics are given, Spock jumps into warp to get the red matter on board well away from anything it could endanger; as a handy side-effect, this also serves to draw the Narada away to a location where it can be taken out safely. Given that, Spock would most certainly have ensured that he came out of warp well away from any major celestial bodies; the most logical place would be to emerge somewhere outside the solar system.
Tailkinker ★