Other mistake: At the start of the episode, someone goes up to Dr. Declan and shows him an iPad that has footage of Black Bolt getting arrested by the police from the previous episode. But the footage he sees is heavily edited, cutting actual footage from the episode complete with the close-up of Black Bolt's face when he gets tased. What he should be seeing is security camera footage from a distance or body cam, not the actual episode moment.
Plot hole: In Agents of S.H.I.E.L.D, Gordon's teleportation ability is tied to sensing and linking with other Inhumans on Earth after their Terrigenesis. Yet in Inhumans, members of the Royal Family such as Triton travel to Earth. If Gordon's powers truly let him detect Inhumans, he should have sensed Triton's presence once he arrived. The show never explains why Earth Inhumans and Moon Inhumans can't detect or acknowledge each other, making this a continuity gap between the two series. The Inhumans reference the Terrigen being set loose in the Earth's oceans at the end of S.H.I.E.L.D season 2, meaning this show takes place at the same time as S.H.I.E.L.D season 3, and there is continuity between them. Yet somehow Gordon is unaware of the other Inhumans from the moon.