When they beam aboard the ship, the characters are masked by holograms that make them appear to be different species that they are. However, for Saru, the resemblance to a human is more than holographic-- he comments that his heels are touching the ground before he even is aware of the holographic disguise. He also wonders if his heart racing as a response to heights is the result of a human body.
Characters repeatedly beam through raised shields, something which is supposed to be impossible in Star Trek.
Adira puts the radiation medicine in their mouth before beaming down to the planet so that they would be able to access it the way the landing party had their equipment hidden from them by the holodeck. No one on Discovery was aware of what happened to the landing party, so they should not have known this was necessary.
After discussing their situation upon arrival on the planet, Burnham says they have, "Four hours, starting now." The countdown would have started as soon as they beamed in, so they have a few minutes less than 4 hours by this point.
One of the bridge crew mispronounces Lr. Nilsson's name as "Nielson."