"Firefly": Episode "Safe" Trivia Quiz

Answer: Zac Efron

Zac Efron made his debut in a brief appearance as Simon Tam as a young man in a flashback scene. He would go on to fame in the High School Musical series.
The flashback scene shows the interaction between Simon and River when they were children, and illustrates the pressure that the young man had from his well to do, expectant father.

Answer: Cattle

During the previous episode "Shindig", Mal makes a deal with a rancher to deliver a load of cattle to the border planet. As so often happens in the series the deal goes wrong and a gunfight ensues.

Answer: Blackmarket Beagles

The cattle was so bulky and messy that Serenity's cargo hold is covered in cow droppings. Zoe suggests that in future they trade in something smaller, on which Wash suggests black market Beagles.
Mal also comments that the mess would be much less, after he steps in a cowpat.

Answer: False

Simon enters the store and picks up the plate that Kaylee wanted to buy, asking if they actually charged money for it. He unwittingly proceeds to further insult Kaylee and Serenity, leaving her hurt and heartbroken.

Answer: Shepherd Book

During the vicious gunbattle Mal manages to get the payment pouch that the ranchers dropped. When the smoke clears they find Shepherd Book lying on the ground with a chest wound.
What they don't know yet is that the doctor has been kidnapped by the Hill Folk, so Mal orders the crew to take the Shepherd to the ship for treatment. Wash rushes to town in search of the doctor but returns empty-handed.

Answer: Inara

The Alliance cruiser is the only medical facility within range, after they determine that Greenleaf is more than ten hours away. There is heavy objection against Inara's suggestion, but at the end there are no other options if the Shepherd is to survive.

Answer: Magellan

The Serenity crew arrives at the Magellan expecting trouble, but are surprised when, after initially refusing their request, the Magellan's captain orders urgent care when Book's ID card is scanned. This leads to many questions by Mal and the crew about Shepherd Book's past, which he sidesteps.

Answer: Hodge berries

The hill people kidnapped Simon as they needed a doctor. He soon becomes aware that they are quite superstitious, but continues with his job until River mentions that a mute girl talked to her, causing the village teacher to become very upset and accuse River of witchcraft.

Answer: Witchcraft

Simon desperately tries to explain to the teacher that River is not a witch, but they are dragged to the village square and the village leader decides she is to be burned at the stake for witchcraft. Simon gets on the pyre with her in an act of suicidal devotion.

Answer: "You're on my crew. Why are we still talking about this?"

Mal shows some heart in this exchange, and effectively tell the doctor that he and River are now part of the Serenity family. Of course it doesn't hurt that he is an exceptional doctor and his skills were severely missed when Shepherd Book was shot.