According to the user who posted all the details, Lex Luthor is not seen in the movie, but gets a mention, with it looking like it's setting up the "Man of Steel 2."
He's never shown but he is referenced in the way Norman Osbourne is referenced in ASM. They state in the movie that he is working on a new AI that will "revolutionize technology unlike anything Metropolis has ever seen." My guess it's a nod to Brainiac should a sequel be developed.
More spoilers include mention that Clark Kent will be his normal "farm boy" self we've seen in the past as lines from Perry White are described.
Yeah there are fun moments with Clark's interactions with Perry White as Perry jokes "Well Clark, I guess you prove all farm boys grow up to be big and strong but still can't to a woman without a stutter." Also, his early interactions with Lois are classic Lois/Clark fodder. Yes, he smiles a few times.
And remember the rumor about
Superman battling robots? True.
Yes he does. They slightly resemble the robots from Sucker Punch but look way more realistic and not like cheap CG cartoons like SP. I was sort of let down that they didn't really give him much of a fight and were mainly a "test" from Zod to see if he were truly the son of Jor-El.
Some other mentions:
Definitely the best Superman film in terms of action and acting.
Less "Zack Snyder" slow motiion: I think he was aiming for more normal paced fights and saved the slo-mo shots for more devastating hits in the fights.
Better than Smallville: The story was great. It was definitely different from other Superman movies and even the animated series. It showed how he felt different all his life even as a young kid and his reluctance to become Superman but accepted it when he knew the world needed someone to defend it. (I know people will be say "Well that's what Smallville accomplished". Well this movie conveyed that in a considerably less amount of time with more emotion than the 10 years Smallville attempted to do. And I say that even though I enjoyed Smallville.)
Cavill was great. Definitely the most solid and relatable Superman portrayal. Way better than Routh and slightly above Reeves IMO.