Everyone Wanted to Be on This Ship - S1-E1
Other mistake: The Ark has two rotating sections. The rotation is to make simulated gravity. We see that when rotation stops, and everyone is weightless. But there is no need to rotate. The ship has artificial gravity. The bridge does not rotate, but everyone walks around just fine.
We Weren't Supposed to Be Awake - S1-E4
Other mistake: Alicia puts the vials with the protein in a centrifuge, supposedly in order to mix them. When she's done, she takes a vial and shakes it to make sure it's mixed evenly. However, a centrifuge separates solutions into their ingredients, not mixes them. (00:34:00)
We Weren't Supposed to Be Awake - S1-E4
Other mistake: Alicia puts a square tray with vials into a device that looks like a small cabin. Then we see a supposedly top shot of the device, which is a centrifuge. But in the centrifuge, the vials are held in a circle, not in a square. (00:34:00)