I was surprised to find out that it's a kids show, doesn't seem like it from what I've watched.
Kids' shows aren't what they used to be. Back then, there was less of a tendency to talk down to kids or sugarcoat things. Violence was strictly restricted, of course, but a lot could be implied.
The movie kind of glosses over the one year between Verity Lambert's departure from the show and the decision to retire William Hartnell. Verity's replacement as producer, John Wiles, wanted to ditch the educational aspect and take the show in a dark, serious, adult sci-fi vein while Hartnell wanted to keep it as it was. The clashes that followed included one Companion (that Hartnell liked) essentially being fired on the set, two more being killed onscreen (a first for the show) and a historical episode set during a massacre that sees a potential Companion apparently killed because the Doctor wouldn't save her. The running feud with Wiles (who tried to get Hartnell fired, but the BBC wouldn't hear of it) plus the relentless pace of the show's shooting (which was virtually year-round back then) exacerbated Hartnell's health problems and helped lead to the downward spiral that Wiles's replacement, Innes Lloyd, found Hartnell in when he took over in mid-1966. (Wiles was in almost as rough a shape as Hartnell when he resigned, 'heading very rapidly for a nervous breakdown' as he put it.)