Kennedy looked tanned and rested, while Nixon had been ill and appeared fatigued. The Republican turned down an offer of stage makeup. That may have determined the future of the Nation.
It's often been said that those who listened to it on radio thought Nixon won, while those who watched it on TV thought Kennedy won. I've listened to it (not watched it) on an archival recording (went to the university library, got the dreadful headphones, had to change desks because the plug didn't work, can't believe that all came back to me, lucky you getting to read this minutiae) and also thought Kennedy won it.
He was more prepared, more direct, more poised; at one point Kennedy made some claim about something Nixon said or did in the Senate, and Nixon barked, "I never said that! I never said that!" He came off sounding like a buffoon, which would have been remedied had he prepared some retaliatory bon mot against Kennedy, or even just clarified it cooly and calmly. That wasn't his forté.
Kennedy's remarks in the debate included his statement that the country has to move a bit quickly just to stand still (a Zen koan from the sound of it, referring to the economy). At this point I can't recall whether he drummed a major campaign talking point, that of the "window of vulnerability", a hawkish take on the Cold War which surprises some of the kumbaya set. That hawkish stance was actually Nixon's own window of vulnerability, because Eisenhower had the U2 / Gary Powers incident and the handling of that had been a fiasco; also, Castro had taken over Cuba on Eisenhower's watch, and Eisenhower did just that, stood and watched. Nixon was stuck having to either defend that inertia or try to change the subject.
Of course, Kennedy was born rich (some might argue that he wasn't, because the real fortune came as a result of Joe Sr's gig as the ambassador, during which time he secured an exclusive import license for scotch, and brought it in as Prohibition lifted), went to the best schools, had the best of everything, and after his military service (during which he injured his back, giving him an alibi to be out of the Senate during the vote on McCarthy) never held a job. At all. Of any kind.
Nixon by contrast came up the hard way; had parents who were grocers; lost his own and some investors' capital on a refrigerator car orange juice scheme; lost a brother to TB; wound up a VP to Eisenhower, who couldn't stand him, but distinguished himself by facing down angry mobs in South America, the kitchen debates with Khruschev, and carrying out presidential duties when Eisenhower had his heart attack. There has seldom been a better-prepared president than Nixon.
But he lost in 1960 by about one vote per precinct (average) and lost the California governor race in 1962, then unleashed some ill-considered contempt for the press (ink by the barrel, blah blah blah). I once saw a great clip of Nixon at the 1964 convention, beaming smile, laughing, stomping, clapping, probably during Goldwater's speech, happier than we're used to seeing him. In 1968 in the Pubbie primaries he ran against, hmm, I have no idea; he mended some fences. Meanwhile the Demwits nominated Humphrey, and lost the election by a margin similar to JFK's 1960 win. Strange to think how Kennedy barely won, considering how all-important those debates are sometimes portrayed by the self-serving broadcast MSM.
I saw the video of the first Kennedy-Nixon debate on YouTube yesterday. The duration was just under an hour. Please go to YouTube and type in Kennedy-Nixon and review the video. There were several debates, so it would appear that the events you mentioned were in the later ones, because I didn't notice any major gaffes or uncertainty by Nixon. The first debate was on domestic policy, or at least supposed to be, but Kennedy tried to get Cold War themes thrown into the mix.