I agree that all the bullying incidents we see are through Snapes eyes, and, as far as we know, that was all the bullying that James did.
I think the term Lupin used was that James got "carried away" and I think that's a reasonable way of putting it. He was the cool one that everyone looked up to, and, again, by Lupin's words, "Snape lost no opportunity to curse him", so he had to prove he was on top. It might have given James a more rounded character if one of Snape's memories had been cursing James, and James' reaction to it.
To me James is that person who's captain of the rugby team at school, goes along with all the high jinx that the team does, everyone thinks is really cool, but does sometimes get carried away and go from being silly to nasty, but no one dares tell him that, although he probably knows, because he's so popular.
I wouldn't have liked him particularly if I;d been at school with him, probably kept out of his way, but a lot of people would-what we'd have called the "in crowd".
Snapes redemption I think is badly written, as he's written as too bad a character towards Harry, but also towards Neville, and probably others. In the first book he didn't know Voldemort was returning until the end, so he had no need to try and keep up his death eater image-but he still bullies and picks on Harry-and even assuming it's the James connection, he's dreadful towards Neville too.
It's only right at the end of the 7th book when he's dying you see him sacrificing himself for Harry. And in actual fact he doesn't-he'd have been killed anyway because Voldemort needed him dead.
If she'd wanted to make his "I'm really on Harry's side, but have to hide it" character believeable, he should have been okay in the first year, maybe occasionally snapped when Harry did something that reminded him of James. Think of the scene where he assassinated Harry's character to Dumbledore-Dumbledore's reaction is "you see what you want to see". ie he wanted to hate Harry from the start.
But the real give away on that he really hated Harry is the lessons on oculmancy (can't spell!). He's alone with Harry. Giving him lessons on something that Dumbledore has said is essential. He treats Harry so badly then, when they're on their own, so no need to keep up a pretence. And in doing so could have had both Harry and Dumbledore killed. Not really the sign of someone who really is good.
At best, his bravery in being a double agent (even though he was basically blackmailed into it) only really counterbalanced his behaviour.
Again, to make the redemption of Snape credible he needed to work properly with Harry. He could have worked him really hard and had Harry hating him for that, or been brisk and business like. Harry didn't need Snape to be nasty to him to stop him learning it properly. Other things got in the way, lessons got cancelled for different reasons, Harry doesn't really want to stop the dreams anyway.