The Space Museum seems to get little love from fans, perhaps because it is one of the weirdest Doctor Who stories. It begins in the TARDIS, with the four time-travellers still dressed in their ancient Roman clothing. They are frozen in time at first, but when they materialize, they are dressed normally. The Doctor thinks they have gone back to a time before their visit to Rome. Vicki drops a glass of water, it breaks, then bounces back unbroken into her hand. When they open the TARDIS door, they find a museum of spaceships. They approach the museum doors without leaving footprints in the dusty landscape. There is absolute silence. The museum doors open, and two museum guards come out and pass them, conversing soundlessly, without seeing them. Inside is a vast collection of technology from many different planets. They are disturbed to find a Dalek shell behind a sign: Dalek. Planet Skaro.
Two young men in black clothing walk by them without noticing them. Vicki finds she can put her hand through a museum display, as can they all, and The Doctor realizes they are not really there. Then they discover themselves frozen in display cases. The music sounds suspiciously like the theme from Twilight Zone. The Doctor believes the TARDIS has jumped the time-track and emerged in the fourth dimension—whatever that means—and they will eventually arrive and end up on display, unless they can alter time somehow. Suddenly the glass fallen from Vickie’s hand breaks, the guards find the TARDIS and the time-travellers’ tracks in the sand, and the figures in the display cases disappear. The Doctor declares they have arrived.
The scene shifts to the Museum Guard’s office, which is also the office of the Morok Governor of the Planet Xeros. Governor Lobos (Ivor Salter) is bored and complaining about his job until he is told there are uninvited visitors who may be rebels. The scene shifts to the rebel headquarters, hidden in the museum, where they have learned that the Moroks have found a spaceship, and they believe help for the revolution may be at hand.
Meanwhile, the visitors are stealing weapons from the display cases, while they search the maze of corridors for the TARDIS, hoping they can escape before they are put on display, but they are constantly arguing about which way to go. The rebels find them, a door opens, and The Doctor is seized by the rebels. The others search for him, arguing about everything. The Doctor comes to, knocks out the rebel guard, but he is then caught by the Moroks, locked in a room, and interrogated by Lobos. The authorities decide The Doctor should be frozen and put in the Museum.
The rebels and the Moroks, separately, try to open the TARDIS but they cannot. We are beginning to realize that everyone on the Planet Xeros—the militaristic Moroks, the servile Xerons, and the Governor himself, bored and dreaming of past Morok glories—are all incompetent. Ian gets the drop on all of them and defeats them easily. Vicki, when she is seized by the rebels, takes over their rebellion out of sheer boredom, tricks the computer into opening the armoury, and leads them to victory.
The entire story is played for humour, but the humour might have been a little too subtle to work. I had to watch it twice before I realized that it was a mixture of Salvador Dali, Absurdist Drama, and Monty Python.