To me, the central issue with using Jughead to stop the Incident occurring in 1977 is that it results in a paradox – how can the Losties be on the Island to stop the Incident if it is the Incident occurring that placed them on the Island in the first place? There are 2 ways to resolve this paradox. Firstly, the Jughead plan didn't work and the Incident still occurred, thus removing the paradox entirely. Or, secondly, the plan did work and the entire timeline is rewritten to remove all contradictions. This may be what we are seeing in the final season of the show.
In the first instance, the bomb detonates but does not stop the Incident, perhaps even magnifying it's effects. The fact that the Losties shift forward in time may be a necessity of keeping paradoxes from the timeline, or it may simply be an aid to storytelling by having all of the main characters back in the same time.
In the second instance, the bomb detonates and the Incident is stopped, which stops the Losties from ever getting to the Island, meaning that all of their interactions with the Island and it's inhabitants can no longer have happened. Thus, the timeline needs to be purified, including all time periods that the shifting Losties visited. Remember that it was Faraday in 1954 that warned the Others about the radiation leaking from Jughead, with Sawyer and Locke also in that time period. If the timeline is to be purified, then it is likely that Faraday would not be there to warn the Others, which may have resulted in them accidently detonating the bomb, leading to the Island being on the bottom of the ocean in the 'purified' timeline. The key clue here would be that the statue we see under the water only having the foot/leg intact, hinting that whatever put the Island at the bottom of the sea did not occur in Ancient times.
In this second instance, Charles Widmore would have died on the Island in the 1950's, thus would not have been able to father Penelope, changing the path of Desmond's life (thus on Oceanic 815 and not in a sailing race). He was wearing a wedding ring however in the 'purified' timeline, so this theory may be killed off if we see that he is married to Penny.
However, there are some other hints to major changes in the 'purified' timeline. For instance, in the original flashbacks we saw that Hurley felt that his lottery win had cursed him, and had brought him nothing but bad luck. But on the 'new' Oceanic 815 flight, he said that he was the luckiest guy alive, and there seemed to be no hint of irony there. Quite how Jughead could have changed this though I'm not sure about.
There could of course be another interpretation of the 'purified' timeline – what if it is a flash-forward rather than a 'flash-sideways', in that the Jughead plan failed to change the timeline, but the Losties will succeed in changing the timeline at a later date. This may explain why we are seeing such large changes in the 'purified' timeline, more than we'd expect from just Jughead stopping the Incident. If they manage to help Jacob win the fight on the Island, maybe their reward is his intervention in their lives to steer them to happiness by stopping the Oceanic 815 crash and putting them on their chosen path - Kate helping Claire raise Aaron (from the scene in the taxi), Jack removing the injustice put upon Locke and allowing him to walk etc?
I was a firm supporter of WHH (Whatever Happened Happened) in the theory wars from last season, but I think it's time to lay down arms on that front, and admit that PCC (Past Can Change) is the way forward…!