Recently I picked up Season 2 of this series and I've been really enjoying it. I hadn't seen this since reruns in the early '70s.
I reviewed the first two seasons on my blog a while back. Haven't gotten around to the third yet. I feel the first season was the strongest; oddly, the showrunner seemed determined to embrace a formula that suppressed the character development and flexibility of format that made the first season so much more interesting. It quickly reached a point where nothing ever really went wrong with the team's plans except for minor problems that cropped up 30 seconds before a commercial and were resolved within 30 seconds afterward. Anytime the plan seemed to be going awry, it turned out to have been part of the plan all along. No surprise that the strongest 2nd-season episodes included the two formula-breaking ones where they weren't on a formal mission but dealing with a crisis they stumbled into, and had to improvise more. Along with "Trial by Fury" (with Paul Winfield and shot on the
Hogan's Heroes sets), a mission that relied more on psychological persuasion than the usual gadgetry and precision timing.
I remember when the first Tom Cruise remake came out. At the time I felt they missed the boat completely. They made the Jim Phelps character a traitor?

Then it's a lot of over-the-top action and overdone explosions. I didn't bother with any of the sequels.
The movies are nothing like one another. Despite the shared title and lead character (or two, Cruise and Rhames), each movie is very much characteristic of its own director's distinctive style. The first is a Brian DePalma spy thriller full of deceit and intrigue, the second is a John Woo spy thriller full of over-the-top action, and the third is a J.J. Abrams spy thriller that's basically
Alias, a mix of larger-than-life, sexy spy action and reasonably engaging character drama. So you can't really use any one of the films as a precedent for judging the others. M:I:III is definitely the best of the three (or rather, the only good one), and the most faithful by far to the original, though mostly in the first half.
Rollin Hand shouldn't be able to do a McGyver and make perfect masks within a half hour or so with only the contents of a kitchen or small town doctor's clinic.
In the series pilot, the masks were treated fairly realistically; Rollin was brought on specifically to imitate someone he closely resembled already, and when he had to double Dan Briggs (Phelps's predecessor) later, it was a far more imperfect doubling and he had to wear sunglasses and avoid speaking so he wouldn't give it away. But the masks were treated more and more fancifully as time went on, so that by the late first season, an enemy spy was able to use a mask to impersonate another man for
weeks, eating, sleeping, sweating, and even undergoing shock therapy through the mask, all without damaging it in the slightest.
It's also quite repetitive the way Phelps is shown choosing his team since he's usually choosing the same people. I like it when an additional unfamiliar face is chosen for an assignment. If done for television today than I think you could get away with a smaller group of core characters and more unfamiliar faces chosen for specific assignments perhaps on something of an irregular basis.
That was the original idea, and there was a lot more team variation in the first season. At the very start of the series, it seems as though the intent was that each episode would have a featured guest team member or two who would be the dramatic focus of the episode -- Martin Landau and Wally Cox in the pilot, Albert Paulsen in episode 2 (as an alcoholic friend of Briggs's whose reliability was in question), Mary Ann Mobley in episodes 4-5 (as an old friend and romantic interest for Briggs). (The dramatic focus in episode 3 was the villain, played by Fritz Weaver.) But Landau's initial guest spot went over so well that he was promptly brought in as a near-regular and quickly became the de facto lead, especially once Steven Hill (Briggs) began having conflicts with the producers and scheduling problems due to his Orthodox Judaism (he wouldn't work at all on the Sabbath). Still, there were a number of first-season episodes that only had 2 or 3 team members aside from Briggs, and a number where Briggs just did the setup and didn't come along. There was one episode, "Elena," where Rollin and a guest of the week were the entire team (particularly striking given that Landau was still technically a recurring guest star), and another, "A Spool There Was," that just had Rollin and Cinnamon in the field.
So in the first season, the dossier scenes in the opening served a purpose, establishing the different team compositions in each episode. In the second season, though, the team composition became much more standardized, so the dossier scenes became redundant, and were dropped at the very end of the season, rarely if ever to be used again. (The 1988 revival series had a dossier scene in the first episode, and that was it.)
It also strikes me that some of their assignments fall out of the purview of espionage and counter-intelligence and were more straight law enforcement matters.
In later seasons, as spy stories became less popular due to espionage scandals and such, the focus of the show shifted almost exclusively to crimefighting, with the Voice On Tape constantly explaining that the villains of the week were beyond the reach of "conventional law enforcement."
It's also fun to spot the Star Trek alumni particularly since the two shows were being made practically next door to each other.
No "practically" about it. They were shot on literally adjacent soundstages, and used the same Forty Acres backlot in Culver City (at least when they were at Desilu).