Stories about time travel frequently mention, and are sometimes focused on, the most famous of all time-travel paradoxes, the Grandfather Paradox:
Say you were able to go back in time, and in doing so, caused your grandfather to die before meeting your grandmother and giving birth to one of your parents. You create a paradox in which, since one of your parents isn't born, you can't exist to go back in time to kill your grandfather, but if you don't exist to kill your grandfather, nothing stops him from meeting your grandmother and giving birth to your parent which means you do exist to go back into time...
Pretty mind-bendy, eh? Well, after watching the animated Justice League season one ending episode, The Savage Time, I've found a different, somewhat less mind-bendy paradox.
I should start by saying that the DC Animated continuity of the Justice League and its characters is fairly different than the continuity of all other appearances of the DC Comics characters depicted. In both the original Wonder Woman comic book as well as the 1970's television series, Wonder Woman and Steve Trevor worked together against their mutual enemies. In the Justice League animated series, however, the princess Diana of Themiscyra takes up the Wonder Woman regalia and departs for 'man's world' in the initial episode, Secret Origins. The Wonder Woman of this story universe doesn't meet Steve Trevor until traveling back in time to attempt to undo a change that allows the Nazis to win World War II. (No superhero team's story arc is complete until they've visited Nazi World, after all.)
So the Justice League goes back in time, helps defeat the Nazis, and returns to the present. The episode (and the first season) ends with Diana going to a veterans' home to see Steve Trevor.
How does Steve Trevor respond? That's the crux of the paradox.
To Wonder Woman, almost no time has passed since meeting Steve Trevor as a dashing ex-spy in the past and seeing him again in the veterans' home in the present. To Trevor, however, decades have gone by, most of which didn't include a Wonder Woman at all. Here would appear to be the options:
a) Either Trevor remembers Wonder Woman enough to recognize her when she first appears as part of the events of Secret Origins and helps found the Justice League, in which case he might legitimately wonder why she didn't visit sooner, or
b) Trevor doesn't remember Wonder Woman ever existing until the moment she returns from the past, in which case it makes perfect sense.
The former isn't such a big problem. The latter, however, is. If Wonder Woman's changing of the past back to its original shape erases her existence prior to her return from the past, then the world she's returning to isn't the same as the one she left -- for starters, where does she come from now, since no one on Themiscyra will remember her?
What about previous Justice League episodes, where the League was only successful because of her presence (as in Secret Origins)? Or other episodes where the League only learns what's going on because of Wonder Woman's actions (as in Paradise Lost)?
Of course, it's not a paradox if version a of events above is true. But in that case, why is Trevor so happy to see Diana?