Forest wouldn't be able to get ahead of Arsenal unless we see any surprise. They don't even need to do that in the first place. 
They are already in a great place in the PL. The 3rd place must be feeling like a dream for them.
I also believe nobody expected them to finish within the top 6 at the start of the season. I can understand having more expectations after seeing how well their form is in the early and mid-season, but I think finishing third or even fourth is a very great result for them. The question becomes how long they can sustain that. If Forrest changed their target to finish inside the top 6 every season, they need new players if they want to compete in the top 4 and Europe at the same time. Hard to imagine other clubs won't target their weakness better next season. We also know from history that overachieving teams can fail to maintain the result, sometimes even doing worse. CMIIW. They are already in a great place in the PL. The 3rd place must be feeling like a dream for them.