It takes any actor playing The Doctor a few episodes to find his feet in the role, and probably just as long for the production team of Doctor Who to adjust to their new leading man. After having Patrick Troughton play an aloof and scheming Doctor in his debut story, in The Highlanders, it seems that the producers are willing to let Troughton loose and indulge his flair for dressing up.
I'll mention this more in following entries (as The Doctor chooses more than one disguise over the course of this story), but in this first episode, he quickly adopts a German accent (and a questionable one at that) in order to try and fool his Redcoat captors that he is a doctor from Hanover. Much silliness ensues, but it can never be said yet that The Doctor is the driving force in the proceedings. The dressing up just gives him something to do while the rest of the characters drive the plot along.
This is Jamie McCrimmon's first episode, but he doesn't attract a great deal of screen time yet. It's weird to think at this stage that Frazer Hines will be in every Troughton episode from here on - quite a feat indeed!