Continuity mistake: After Flash fixes the timeline, he is back in Bruce's Batcave and gives Bruce a letter from his father. Bruce is working at a station and his utility belt is there as he is working on it. When the camera pulls back before Flash runs off, his utility belt vanishes. (01:17:00)
Revealing mistake: During the flashback when we see Bruce Wayne murdered, Thomas Wayne is beating up Joe Chill while in the background, Martha can be seen cradling Bruce's dead body. As she picks him up though, the animators forgot to remove the still frame so it appears as if there are two corpses.
Answer: Flash couldn't travel through time later in the movie not because Zoom was alive but because Zoom was also tapping into the Speed Force, preventing Flash from gathering enough of the Speed Force to break the Time Barrier. When Flash originally went back in time it's likely because Zoom was in custody, therefore not tapping into the Speed Force at that time.