Based on watching Finland's semi-final and bronze medal games, I'd say that Puljujarvi's game has improved over the course of the year. Other than his stupid penalty that led to a goal against, I wouldn't say there were many specific mistakes he made. Most of his play was competent but definitely not brilliant. Two things that seemed like potential improvements to my (untrained) eye:
1) Try playing with a shorter stick: Some guys, like Laine and Aho can play with really long stick and use them to gain an advantage. Puljujarvi plays with a really long stick but he doesn't really use the extra reach to his advantage and it looks like it has a detrimental effect on his puck handling, puck battles and ability to get his shots off quickly. Those extra inches on the stick may come in handy when taking a slapshot, but it looks as though he has no clue what to do with them the rest of the time.
2) Improve Conditioning: It's obvious he gets tired too early in his shifts, although maybe if he was a smarter player he wouldn't spend so much time chasing the puck and would have more energy. Hopefully this can be remedied with training, although I know it has been a criticism of Puljujarvi for years.
These aren't the main things holding him back, but they're relatively easy fixes compared to things like improving hockey IQ.