Things that stood out to me:
* Alfred muttering under his breath. This doesn't translate well to the screen, IMO. Makes him look crazy. On that note, Alfred comes across as the Batman's butler, rather than his surrogate father, confidante and friend. Yes, being a butler is his occupation, but it doesn't really cover what he means to Batman. The rest of his dialogue comes off rather stunted.
* Work on synonyms. 'Compete' and 'competition' feature rather heavily in the Amazon dialogue and are jarring. Same goes for 'prophecy'. Their dialogue as a whole doesn't sound very, I don't know if sophisticated is the right word, but I'd expect more rigid speech patterns.
* Clark sounds a little too much like a boyscout. 'Gee' and 'golly' aren't bad, but not together in about three seconds. 'Swell' just comes across odd when he uses it again in 'Swell to be back here'.
* On that note, the dialogue with Ma Kent feels unnatural. I don't really think you got her character right.
* Barry suddenly starting to talk about his 'personal issues' with his colleague doesn't come across as very believable. This might change from page to screen though, as it can also depend on the actors. As it is though, going off the dialogue that this is just a random colleague: a little weird.
* As has been said, Barry's not a punk, which you made him sound like in that fight with Cold.