The whole premise is awful. First, nobody in their right mind on a decontamination team would remove their glove and reach inside their "helmet" to scratch their nose (especially since the flexible helmets would allow this to be done from the "outside"; we won't comment on the complete non-air-tightness of the helmets). Second, the planet's mass would not change. Third, the orbit wouldn't decay, unless they were actually in the atmosphere and experiencing friction. Fourth, even if we allow the "going backward in time" concept (as was done in other episodes), Kirk still has failed in his obligation to Starfleet to observe the breakup of the planet. The first time through time (if you'll pardon the expression), they were too busy trying to fix the problem of the crew to make the observations they were required to make. Kirk should have used this opportunity of getting a second "pass" through time to go back and make the observations he missed the first time. He's going to have a bit of a problem explaining to Starfleet why he went on to his next destination without fulfilling his mission, even if he does have partial records from the observations on the first "pass" through time.
Review of The Naked Time
