We already have one of these for TOS, but I thought it might be fun to start up a similar thread for TNG. Things you'd never noticed until a recent rewatch, despite them being there all the time. 
Here's three I noticed for the first time when I recently rewatched season one on Blu Ray:
- In the pilot episode "Encounter At Farpoint", Picard actually suggests that Q use their upcoming mission (ie, the whole thing) as an ongoing trial by which Q can judge their actions. Q doesn't dismiss the idea, he simply refocuses the conversation on Farpoint alone. But in "All Good Things...", we do discover that he took Picard's suggestion to heart, and the 7 year mission was an ongoing trial.
- The Romulan disturbance in "Angel One". For many years I thought this was some kind of continuity error, as there's some considerable separation between all the talk here about possible Romulan attacks on Federation outposts along the Romulan Neutral Zone and the Enterprise racing off for a confrontation with Romulans by episode's end, and the resolution of that story in the season-ending "The Neutral Zone", where we are told this was the first contact with Romulans in decades. But on my recent rewatch, I realized that all the talk is about the attacks, and the possibility of it being the Romulans, not necessarily that the Enterprise was actually going to face off with them. It seems likely that they went off to investigate the attacked outposts but did not find any Romulans at all, which makes it consistent with the season-ender. (It does, however, potentially leave Picard's remark in the later "Heart of Glory" a continuity error, where he claims they haven't heard of the Romulans in a very long time.)
- In "Coming of Age", Riker's anxiety over Admiral Gregory Quinn and Commander Dexter Remmick coming aboard to investigate the Enterprise crew. In context it just looks like he's perturbed about the crew being accused of something they haven't done, but with the broader picture of how Riker had been harboring guilt over his role in the Pegasus affair all those years, maybe he was really afraid that his dirty little secret had been uncovered? Adds a little frisson to those scenes.
Here's three I noticed for the first time when I recently rewatched season one on Blu Ray:
- In the pilot episode "Encounter At Farpoint", Picard actually suggests that Q use their upcoming mission (ie, the whole thing) as an ongoing trial by which Q can judge their actions. Q doesn't dismiss the idea, he simply refocuses the conversation on Farpoint alone. But in "All Good Things...", we do discover that he took Picard's suggestion to heart, and the 7 year mission was an ongoing trial.
- The Romulan disturbance in "Angel One". For many years I thought this was some kind of continuity error, as there's some considerable separation between all the talk here about possible Romulan attacks on Federation outposts along the Romulan Neutral Zone and the Enterprise racing off for a confrontation with Romulans by episode's end, and the resolution of that story in the season-ending "The Neutral Zone", where we are told this was the first contact with Romulans in decades. But on my recent rewatch, I realized that all the talk is about the attacks, and the possibility of it being the Romulans, not necessarily that the Enterprise was actually going to face off with them. It seems likely that they went off to investigate the attacked outposts but did not find any Romulans at all, which makes it consistent with the season-ender. (It does, however, potentially leave Picard's remark in the later "Heart of Glory" a continuity error, where he claims they haven't heard of the Romulans in a very long time.)
- In "Coming of Age", Riker's anxiety over Admiral Gregory Quinn and Commander Dexter Remmick coming aboard to investigate the Enterprise crew. In context it just looks like he's perturbed about the crew being accused of something they haven't done, but with the broader picture of how Riker had been harboring guilt over his role in the Pegasus affair all those years, maybe he was really afraid that his dirty little secret had been uncovered? Adds a little frisson to those scenes.
