Presumably, Agnew still gets forced out and Ford takes over as VP. Nixon, politically wounded and unable to accomplish much, serves out the last of his term through to '76. Ford, presumably, runs for the nomination, but it's unclear he can get it without the imprimatur of being the incumbent. Given how close it was, it's probably not unreasonable to guess that Reagan takes it. Carter can still ride the anti-establishment wave (which would probably still be there, but not as strong), so we get Carter vs. Reagan in '76. This is a tough call - Carter barely squeaked out a win against Ford, and Reagan was a phenomenal campaigner. I suspect Reagan's better campaign skills would offset the loss of incumbency and still call this a narrow win for Carter.
We'll assume no other major changes through to '80. So...Reagan runs again, but does he get it? American political parties haven't been fond of giving second chances at the Presidency in the recent past - the last time a losing candidate was renominated four years later was Adlai Stevenson in '52 and '56. In our world, he won this one definitively, so I'd be tempted to say he pulls it off but with more competition, maybe co-opting Anderson as a VP pick instead of Bush.
That's as far as I've gotten so far. I may play with this idea some more, or possibly take it down an alternative leg of the trousers of time: what if Reagan won in '76?