OK, this timeline has gone on for an extremely long time without a summary, so I will provide the Reader's Digest version of all the major events in this timeline for those who don't want to read 23 pages of posts.
1. IRL, Star Trek was placed in a 10 PM Friday night time slot in its third season by NBC in order to kill the series. ITTL, Star Trek is given the Monday 8:00 PM time slot, where it is able to thrive because it attracts a different audience than Gunsmoke, CBS's famous Western in that timeslot.
2. In exchange for pleasing all the rest of the principals involved in this 8:00 PM time slot, NBC tells Gene Roddenberry to take a break from the series for a year to handle personal matters, and to get Roddenberry out of the way, because he's always been fighting with the network. Robert Justman, who was associate producer of Star Trek IRL, becomes the executive producer, and he hires D.C. Fontana to run the creative side of things. Justman has a much better working relationship with NBC ITTL than Gene.
3. Justman ITTL tasks Fontana to write the series as more of an action adventure space Western than it was in its first two seasons, and Fontana creates an arc of six episodes (a Federation-Romulan conflict) that captivates the television audience. The last of the six episodes is a story which involves Lieutenant Uhura taking command of the Enterprise in an emergency and fighting off the Romulans, ending the arc. The viewing public and television critics view this episode as historic because it places a temporary all-female cast in traditionally male roles, and expands the show's popularity.
4. Star Trek builds a massive audience on par with the top shows of the period in its third season, because it beats the competition on ABC and its audience does not cross over a whole lot with Gunsmoke. Star Trek starts to win ratings battles from time to time and becomes a top 10 show.
5. ITTL,the show develops so much of a following that even the legendary Cary Grant wants in for a couple of episodes to start the fourth season. Star Trek becomes arguably the top show on television in season four, winning four Emmys, including one for best series. Leonard Nimoy wins an Emmy for best supporting actor, David Gerrold wins an Emmy for an episode he writes called Tomorrow Was Yesterday, and Matt Jefferies and the technical crew win for special effects and set design.
6. However, the cost of producing the Federation-Romulan conflict in the third season causes the series to run one episode short, and the cost of the big guest stars (Grant, Milton Berle, and Ann-Margret) in the fourth season causes the show to go over its budget ITTL. Paramount executive Doug Cramer, in charge of the series, fires Justman in the middle of the fourth season, but the Star Trek actors, upon hearing this, go on strike and save Justman's job for most of the rest of the season.
7. At the end of the fourth season ITTL, Roddenberry wants back in and has a meeting with Cramer, who fires Justman, this time for good. William Shatner is fed up and goes public with his complaints. This causes Cramer to want to cancel the series on the spot, but NBC wants another season of Star Trek because it is winning ratings battles. Cramer acquiesces and green-lights the fifth season. Cramer eventually becomes a fan of the series and produces a Star Trek TV movie after the series is cancelled.
8. Shatner and Nimoy are actually OK with the series ending after 5 years. Shatner wants to be a big movie star and Nimoy doesn't want to play Spock anymore, and leaves in the middle of the fifth season. ITTL, Will Decker and Xon, who are characters in the aborted Phase II IRL, become part of the second half of season five ITTL. A young Tom Selleck is cast to play Decker.
9. Star Trek reunites the Beatles for a world tour in 1971. Paul McCartney and John Lennon decide to appear in the fifth season premiere, and resolve their differences.
10. ITTL, DeForest Kelley wins a best supporting actor Emmy for season 5, but the show fails to repeat as best series, although it is nominated.
11. ITTL, Shatner is shut out of major movie roles because he went public with his complaints, but eventually becomes Steve Austin on The Six Million Dollar Man.
12. IRL, Shatner is the most decorated TOS actor. ITTL, Nimoy becomes the most decorated TOS actor, because he lands a role in Fiddler on the Roof and wins a Best Supporting Actor Oscar to go with his supporting actor Emmy.
13. DeForest Kelley ITTL goes on to become Peter Falk's sidekick in Columbo.
14. James Doohan ITTL voices cartoons for a few years and finally lands a movie role as the villainous husband in The Stepford Wives (1975).
15. George Takei goes into politics and wins a seat on the LA City Council.
16. Walter Koenig writes a book about Russian inventions that is critically acclaimed by the New York Times.
17. Nichelle Nichols goes back to Broadway after a role in SHAFT, where she collaborates with Isaac Hayes on his album. She declines all future blaxploitation movie roles and lands roles in Grease (and will land a starring role in Chicago in 1975, where she will become a huge Broadway star).
In politics:
1. Instead of continuing Vietnamization IRL, President Nixon expands the war in Vietnam in an effort to win ITTL, causing the Republicans to get walloped in the 1970 midterms. Nixon is able to produce an armistice right after the 1970 midterms ITTL, but it doesn't hold as North Vietnam's Le Duan is assassinated and Nixon's CIA overthrows the South Vietnamese Thieu government for Nguyen Cao Ky in April 1971.
2. Nixon goes to China in 1971 in order to preserve the peace in Vietnam and open up China. IRL, Nixon went to China in 1972.
3. When the Vietnam War resumes in May 1971, the US Army and South Vietnamese are ready for the North, and fight off their offensive. Operation Linebacker I and II occur in 1971 and early 1972 ITTL. IRL they both occur in 1972.
4. Nixon's apparent success in Vietnam is still not rewarded by the American public, who have turned against the war irretrievably. The economy suffers two recessions, in 1971 and 1972. The 1971 recession actually occurred IRL, but there was no recession in 1972 IRL.
5. Watergate occurs as IRL, but the Democrats capitalize this time on the scandal, because they nominate Edmund Muskie ITTL instead of George McGovern. The 1972 presidential campaign is extremely close most of the way, with Nixon holding a narrow polling lead.
6. Spiro Agnew's kickbacks scandal breaks during the 1972 campaign. IRL, it did not break until 1973.
7. Nixon's dealings with Anna Chennault are revealed towards the end of the 1972 campaign ITTL. IRL, voters in 1972 did not know about this.
8. Edmund Muskie ITTL wins a cliffhanger election against Nixon. California is the decisive state and Muskie wins by a couple of thousand votes out of 8 million cast.
9. Nixon believes there are hijinks in California and files a lawsuit that goes to the Supreme Court ITTL, like Al Gore in 2000 in Florida IRL. Nixon loses the case and Muskie is elected.
10. Muskie passes a Medicare expansion that covers all American families, and environmental reforms that clean up big business.
11. Nixon is indicted for conspiracy and obstruction of justice ITTL due to his actions regarding Watergate, as the tapes are leaked in 1973. IRL, we didn't know about the tapes until the Supreme Court forced Nixon to turn them over in 1974.
12. Ronald Reagan thinks President Muskie is weak on communism ITTL and is considering a 1976 run. With no GOP standard bearer, it is likely that Reagan will be the frontrunner. IRL, President Ford narrowly won the 1976 Republican primary over Reagan.