He should be more villainous and less humorous this time around as well.
JJ's belief in the Raimi movies was that Spidey was simply posing as a do-gooder in order to shift the blame on others while he was the real criminal himself. JJ's issue was that he didn't trust heroes, and it's understandable, giving he gets to the dirty truths of supposed heroes out there in his line of work.
But to reflect on modern times, as newspaper sales drop in favour of online stuff, JJ should be looking to accuse Spider-Man of crimes, simply to boost sales of his paper.
To see Spidey's rep go down in the sequel, would be a nice touch, considering what he's already going through.
And if the Symbiote manages to corrupt him, if that storyline comes to fruition, it gives JJ ammunition to use. It'll cause the police to side with JJ, and cause the city to fear and hate Spidey.
I'm getting bored of the city always praising him. It's just repeating what the Raimi movies did.