This is a (fairly) big budget movie that could have been a lot better. It is also a poor transfer of Kipling's novel to the screen, for a variety of reasons.
The raison d'être for this movie would appear to be the competition that television was posing at the time. One of the things Hollywood did to lure audiences away from their little box at home was to give them things that the TV could not provide: bright Technicolor, as in this movie, and often, colorful travelogues, either as short features between movies or as part of the movies themselves. The most famous example of this is Around the World in 80 Days, with used Verne's novel as an excuse for shooting colorful and exotic scenes around the world. This movie, if you watch the trailer, was presented as that, though it doesn't deliver the way Around the World did. A lot of the scenes are, quite obviously, either filmed on a sound stage altogether or filmed on a sound stage and then projected against film that was shot in India. Unfortunately, in both cases the result looks strangely amateurish for a big studio, big budget film. The landslide scene near the end that kills the rebel soldiers is probably the most obvious example of bad use of back projection, but there are others.
The fact that the visuals were meant to be the big attraction may account for the fact that other aspects got short-changed.
First, the casting.
I disagree with some of the other posters on here. Dean Stockwell is generally inadequate as Kim. Far too often he just rushes through his lines as if they had been learned by heart and not understood. He's good in the last scene with the dying Lama, but too often he doesn't seem to be a real person expressing his feelings; he just sounds like a mediocre actor reciting lines.
Part of the problem here, though, are those lines. The dialog is far too often stilted when it shouldn't be. In the novel, Kipling makes it very clear when his characters are speaking their native language, which they of course speak fluently, and when they are speaking a language they have learned (usually English) and over which they don't have the same command. The movie never bothered to figure out how to do this, and sometimes the characters speak in a very stilted fashion when they would clearly be speaking their native language, which makes them look foolish even when the lines are well delivered.
Another problem with Stockwell that is not his fault is that the time frame of Kipling's novel has been truncated. In the book, Kim goes to school for three years, aging from a child of 15 to a young man of 18 before he gets involved in the intrigue at the end. This makes it quite believable in the novel. In the movie, Kim is still barely 15 when it all takes place - I assume so that they did not have to get another actor to play the older Kim - and it stretches credulity. To make matters worse, Hurree Chunder is killed off, unlike in the novel, so Kim is left to organize a lot of the dealings with the Russian and French spies, which really strains belief.
Chunder is probably killed off so that Mahbub Ali (Errol Flynn) can play a more important role than in the novel. He, rather than Chunder, now organizes the routing of the Russians - though that episode is completely rewritten and becomes much less interesting - and not at all funny, which it is in the novel.
It's also unfortunate that Chunder is killed off because Cecil Kelloway, who plays him, definitely gives the best performance in the movie. Flynn could have been great had he exuded the same charm and charisma that made him a star in the 1930s, but we seldom get to see any of that in this movie. The obvious comparison would be The Prince and the Pauper, in which Flynn also played against a boy who faced great travails. There he was at his best, as were the Mauch twins, who do a much more natural job of delivering dialog than Stockwell does.
The change from the novel that I found most aggravating was the end. (Spoiler alert here.) In the novel, the Lama comes to an understanding of the goal he has been seeking, actually finds a river, and then comes to understand the nature of the river he seeks, which could be anywhere. He is quite alive at the end of the novel, and explains his entire philosophy in a very moving fashion. Kim will now have to decide, having finished school, whether he will continue to follow him or go back to the English. In the movie, the Lama has the hallucination of a river and dies, which makes him look crazy. Mahbub Ali then takes Kim to the English, deciding his future - something that Kipling's Mahbub Ali would never have done. In general, the Lama's role as a philosopher is greatly reduced in the movie, again, I suppose, because the attraction was to be the visuals and not the dialog. Decades later Steven Spielberg showed, with Star Wars, that great visuals did not mean intellectual dialog had to be sacrificed, but Victor Seville, who directed this Kim, was no Spielberg.
So, for those who know the novel, this will be a real disappointment. It could have been better, with that budget, but it would have had to have been given to a better director and not approached as a Technicolor travelogue.
But even for those who have not read the novel, there are too many weak points to make this anything other than sporadically interesting as a movie.