Cute.
Erskine quite explicitly says that the serum amplifies all of the user's traits, for good and for bad, and reminds Steve that he has to actively keep himself in check, to stay good.
And let me make this clear: I agree that Steve mostly succeeds in doing that. He's not a villain at any point. Pre-serum Steve starts out as a brave, good-hearted young man who does have some very visible flaws, and post-Serum Captain America is a brave, good-hearted hero who visibly has the same flaws, but is mostly in control of them.
How exactly does a sickly 75-pound weakling trying to cheat his way into infantry service not constitute a pretty damn clear case of fraud? It's even explicitly on screen; Steve gets caught by the recruiter and is politely but firmly turned away as unfit for service, and despite being unable to improve his unfit health, continued to try to enlist over and over again. Again, the point is not that this made Steve a bad person. It does make him ridiculously stubborn (for good and for bad), and it does show that he completely ignores all reason and logic when he has his mind set on doing something he deems "heroic".
That stubbornness is something we continue to see in Captain America. It's at the heart of a lot of his genuine heroism, but it's also a tragic flaw in the Greek sense, because it means he's too stubborn to admit when he's actually wrong or overlooking something actually important.
