Trivia: Picard's artificial heart is first mentioned in episode 2-17, "Samaritan Snare."
Trivia: We learn in this episode that Picard graduated from Starfleet Academy in 2327.
Since much of this episode takes place in a mindscape either created by Q, or is a near-death hallucination by Picard which may not even involved Q, some contradictions and continuity errors may simply be the result of Picard's mental state rather than actual issues in the "real" Trek universe.
While Picard is sitting in Ten Forward with Riker and Troi, Data calls all senior officers to the captain's ready room. However, just moments later, Geordi tells Picard over the comm system that he's still waiting for his report. Why is Geordi still in Main Engineering and not with the other senior officers?
The episode begins with Picard severely wounded after being attacked and shot with a "compressed terion beam". Later, while in Q's after-life, Picard says "...and I wouldn't have died from a random energy surge...". An intentional shot from a weapon is hardly a random energy surge.
Lt.(jg) Picard: How would you evaluate me as an officer?
Deanna: Well. Um, your performance records have always been good. You're thorough, dedicated...
Riker: ...steady, reliable (searching for something to say) ...punctual.
Picard: I see. What would you say if I told you I thought I was capable of being more than that.
Riker: Frankly, Lieutenant, I don't think that's realistic.
Picard: Why? Please. This is important to me. I know I can do more.
Troi: Hasn't this been the problem all along? Throughout your career, you've had lofty goals. But, you've never been willing to do what's necessary to attain them.
Picard: Would that be your evaluation as well?
Riker: I'd have to agree with Troi. You talk about wanting more. But, when it comes to doing something about it, you hang back. If you want to get ahead, you have to take chances. Stand out from the crowd. Get noticed.
Picard: Having a good laugh now, Q? Does it amuse you to think of me living out the rest of my life as a dreary man in a tedious job?
Q: I gave you something most mortals never experience: a second chance at life. And now all you can do is complain?
Picard: I can't live out my days as that person. That man is bereft of passion and imagination! That is not who I am!
Q: Au contraire, he is the person you wanted to be -- one who was less arrogant and undisciplined in his youth, one who is less like me? The Jean-Luc Picard you wanted to be, the one who did not fight the Nausicaans, had quite a different career from the one you remember. That Picard never had a brush with death, never came face-to-face with his own mortality, never realized how fragile life is, or how important each moment must be. So his life never came into focus. He drifted through much of his career. No plan or agenda. Going from one assignment to the next, never seizing the opportunities that presented themselves. He never led the away team on Millica 3 to save the ambassador, or take charge of the Stargazer's bridge when its captain was killed. And no one ever offered him a command. He learned to play it safe. And he never, ever, got noticed by anyone.
Picard: You're right, Q. You gave me the chance to change, and I took the opportunity. But I admit now, it was a mistake.
Q: Are you asking me for something, Jean-Luc?
Picard: Give me a chance to put things back the way they were before.
Q: Before. You died in sickbay. Is that what you want?
Picard: I would rather die as the man I was, than live the life I just saw.
Picard: There are many parts of my youth that I'm not proud of. There were loose threads--untidy parts of me that I would like to remove. But when I pulled on one of those threads, it unraveled the tapestry of my life.
Q: (As a flower deliveryman) Is there a... John Luck... Pick-erd here?
(Picard has just botched an intimate encounter with Penny)
Q: ...A Penny for your thoughts... you didn't tell me you were such a ladies' man.
Picard: I wasn't. I was a puerile adolescent, one who allowed himself to be led by his hormones instead of his brains. I was more like... like you.
Q: Then you must have been far more interesting. Pity you had to change.
Picard: (to Q) No, I'm not dead! Because I refuse to believe that the afterlife is run by you! The universe is not so badly designed!
Picard: What if I don't avoid the fight? What if I won't make the changes?
Q: Then you die on the table...and we spend eternity together.
Picard: Q, what is going on?
Q: I told you. You're dead, this is the afterlife, and I'm God.
Picard: You are not God.
Q: Blasphemy! You're lucky I don't cast you out or smite you or something.
(Picard worries about altering history)
Q: Please...! Spare me your egotistical musings on your pivotal role in history. Nothing you do here will cause the Federation to collapse, or galaxies to explode. To be blunt...you're not that important!
In "Yesterday's Enterprise," the crew of the Enterprise-C wears Kirk-era movie uniforms minus the turtlenecks and belts. In "Tapestry," Picard wears the same uniform, minus the turtleneck but with a belt. It seems the turtleneck was the first element of Kirk's movie uniform to go. The actors in Star Trek II-VI complained the turtlenecks were very uncomfortable, so it can be assumed the officers would feel the same way and Starfleet eliminated the turtlenecks for comfort reasons.