While Batman vs Superman being pushed into May of 2016 is incredibly disappointing for any fan, I have a feeling there may be a very good reason why they pushed it back.
Lets look at five recent pieces of information:
1. Chris Terrio brought on to “rewrite/polish” the script
2. Batman vs Superman and Justice League rumored to shoot back-to-back
3. The Rock confirms project with DC + other casting rumors for DC heroes emerge
4. “filmmakers time to realize fully their vision”
5. Batman vs Superman still begins shooting relatively early in 2014 (2nd quarter = April)
Now to me, by strictly connecting the dots, I believe that Chris Terrio was brought on board to do a rewrite on the script while David S. Goyer begins prepping a Justice League script. The extra time is needed in order to prepare two movies to be shot back-to-back and thus create “time to realize fully their vision.” And Batman vs Superman still begins filming relatively soon (2nd quarter according to the press release, or 6 weeks from the initial start date according to Batman-News.com). This says that there aren’t really problems with the production on Batman vs Superman but in order to film 2 movies back-to-back they need to get other things in order, and extra planning is required - including how a BvS will lead directly into a JL film (as is rumored) and more importantly: casting the other JL members before their respective schedules fill up.
Of course this is all purely my speculation as we don’t know all the details. The point is, Batman vs Superman is still starting to film soon, we’re still going to get looks at the characters in costume soon, and (hopefully) WB will let us all know what exactly they are planning.