Incorrectly regarded as goofs
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.
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.