Once the last mythos card is flipped, is there no point to continuing the game?
Since most (or all) mysteries require waiting until the end of the mythos phase to officially complete them, is there no point to continuing the game once you flip the final mythos card and still haven't solved the first 3 mysteries?


In theory this is covered by the Reference Guide under Winning/Losing.

In practice, the official errata explains this:


  If a Mythos card cannot be drawn during the Mythos Phase, the Mythos Phase ends. Then, if investigators have not won the game, investigators lose the game.


So what happens is:


The mythos phase skips right to the end.
At this moment a Mystery card may say "At the end of the Mythos Phase, if [something], solve this Mystery". If this was the last mystery, the Ancient One sheet will usually say that you win.
Anyway, the rules say that you lose, because you had no Mythos Card to draw.
BUT the rules also say that if you win and lose at the same time, you win. (again Winning/Losing in the Reference Guide)


So if that was your last mystery, and you solved it, then you win.

As for beating the Ancient One: Yes, if a game component says you win, then you win. That's the actual rule (Winning/Losing).

Waiting until the end of Mythos Phase to win, is not a rule - it's written separately on each Ancient One's sheet.