Remembrance - S1-E1
Other mistake: Picard gives the mysterious girl some Earl Grey. She has it in hand only in one shot, the faraway one when the two Romulan servants are leaving. The way the scene goes, at no point during the whole scene does she have time to even take a sip. (00:19:05)
Episode #1.7 - S1-E7
Other mistake: Surveillance cameras are shown on monitors when the mass panic kicks in even though any chip-dependent electronics shouldn't work in the game world (previously stated by Chotu). (00:08:20)