Yeah, dang it. My biggest problem was the Spider that bit Peter. 
 
Like someone mentioned before, it almost makes it look like anyone could become Spider-Man. 
 
A very slight problem I had was the webbing. Peter developed it himself in the comics, but in the movie he's using Oscorp's tech to make it. It's made worse by the fact that Spidey says "It's webbing I developed" to the car-jacker, but like I said it was a very slight problem I had with it. 
 
One question I did have, in the movie Connors says that no subjects survived the process (I take it he meant the animals, as he made a big stink about not testing on humans just yet) so I was just curious, how did Peter survive the bite?
 
Its especially compounded by the fact that Peter didn't even seem to fear for his life when Connors told him that.
 
One thing I did notice though, did it seem like Rajit Ratha threatened Connors to anyone else?
 
He mentions the accident that took the life of Peter's parents and then says "Richard Parker was saying the same things you are now" (or something alone those lines)
 
So to me it made it seem like Oscorp was involved in what happened to Peter's parents.