I'm surprised nobody is bringing up the biggest implication: the forestalling of Ronald Reagan's career.
Let's say that Nixon runs for, and wins, reelection in 1966. If he then wins the presidency in '68, his Lt. Governor succeeds him. This would likely be George Christopher (R), the former SF mayor, who just barely lost the Lt. Governor's race in '62.
Reagan might run in '70, but he'd be facing an incumbent in the primary and he wouldn't be able to capture the anti-Great Society/anti-Pat Brown zeitgeist sweeping California in 1966. Most likely it's a Christopher (R) vs. Unruh (D) matchup in 1970.
If Unruh wins, he delays Jerry Brown's career and could end up being a serious contender for the Democratic presidential nomination in 1976, quite possibly winning post-Watergate. Maybe we wind up with something like this?
37. Richard M. Nixon (R - 1969-1974)
38. Gerald R. Ford (R - 1974-1977)
39. Jesse Unruh (D - 1977-1985)
40. George H.W. Bush (R - 1981-1989)
41. Pete Domenici (R - 1989-1993)
42. Bill Clinton (D - 1993-2001)
43. George W. Bush (2001-2009)
44. Barack Obama (2009-?)
Of course, it's possible that no Reagan and an Unruh presidency could produce ripple effects that produce a completely different cast of pols today.