Goofs

Earlier in the series we learned that Peter almost drowned in a car accident but was saved by "September". In this episode Peter and Olivia make sure that the "Observers" would never exist. The last scene of the series show Peter and Olivia in a park with their baby. If the "Observers" never existed, it means that "September" could never have saved Peter from drowning and, if he could not have saved him, it means that Peter would have died in that car accident and would never have met Olivia.

However, it was actually revealed that a car accident was simply a story told to Peter; that in reality Walter and Peter fell through the ice after crossing back from the alternate universe.

Continuing this line of thought: If the observers never existed then Walterante (the name for the Walter from the alternate universe) would not have been distracted by September and would not have missed the cure for alternate Peter and therefore Walter would never have needed to cross over to start with, and therefore would not have brought the alternate Peter back to this universe to start with.

However, another episode created a new time line for this universe that eliminated Peter from it. Since Peter "came back into existence" in this altered time line even though he was removed from it and therefore was already existing in a time line and in a universe he did not belong to, it is at least plausible that he could continue to exist after the observers were eliminated from ever existing.

The point of going to the future is to stop the forced evolution of the Observers. Walter and Michael make it to the future and the show ends with the Observers' invasion never happening because the Observers never happened, or at least not in the emotionless form we saw in the show. If that is the case, then September should not have been present at the Lake to save Peter and Walter; both of them should be dead. Also, if September never existed, then Michael never existed, so the invasion would still take place. What we should have at the end is Olivia, without Walter, joining Fringe Division and researching the Plan (an idea dropped early in Season 1). Of course, we could go back as long as the Observers have been observed in history (the historical prints and paintings shown throughout the series), so it is possible that none of this would ever have happened and we could be looking at a completely different time line.

However, if the observers did not ever exist then Walter would not have crossed over to the alternate universe and brought back the other Peter and they would not have been on the lake together and therefor would not need to be saved. The only reason Walter crossed over was because Walternate missed the cure for his Peter because September distracted him.

That actually does not mean the ending could not have happened. It was already established that the Peter at the end of the show did not belong to the current time line of this universe but was present anyway, so simply eliminating the observers would not necessarily also eliminate this preexisting paradox.

In an earlier show, the Fringe team pursued a man who could make paraplegics float using an osmium solution that worked only due to the unraveling of the two universes. Walter then said in the next season that the universes had healed themselves, thereby the laws of physics were once again intact. Because of this, Walter's osmium-tipped bullets shouldn't have made the Observers float when they were shot.