Well first off Nixon has to lose. I suppose the easiest POD is no Chappaquiddick and hence Ted Kennedy runs in 1972 and wins. Perhaps butterflies make Viet Nam go a little worse making it a little easier. (We can have a different Democrat, I suppose, run and win. Muskie, pre-"cry", was ahead of Nixon in the polls a few times if I recall correctly.)
Secondly does Watergate matter as much? Nixon lost, the Democrats are in. Is it worth it to keep following the story or do the editors take them off the case because there's no real point to kicking Nixon around?
If it remains a minor story, America will be better off. The establishment Republican forces will retain some power (i.e. the people who believe in balanced budgets), people's faith in government won't be quite as shaken, and the right-wing war against the press will be at a lower key if at all without Nixon and without Nixon's downfall.
All good things.
If the story blows up that the consequences are around as bad as OTL, in the long-run. Perhaps worse, because with a Democrat in office it looks a lot like helping reporters to kick Nixon when he's down.
Ford will retire as he planned to, Reagan will be the Republican nominee in 1976 (interestingly pre supply-siders), and the Watergate Babies will not exist—or mostly not exist.
Without running McGovern and with the Democrats now being the ones propping up South Vietnam (no Watergate means money/guns keeps South Vietnam existing) they should remain strong on defence in the eyes of the public the way JFK & LBJ were. The Democrats now have the chance to recover their balance they never really got IOTL.
The Republicans may still be hurt by Watergate, but much less so. Reagan may or may not win in 1976, and either way it probably turns out ok.