Trivia: Apart from Picard, the only other characters to appear in all three timelines throughout the story are Worf and Data. The rest appear briefly, or not at all, in either the past or future timeline, but appear in either one or both of the other two. e.g. Troi appears in the past and present but is dead in the future. Riker is also seen in the past, although this was taken from Season 1 episodes.
In the past scenes, they forgot to change the conn chairs to their first season versions, when they were much taller.
In the past timeline sequences, they briefly slip-up and leave in some signs from the future-timeline scenes - look at the turbolift doors just after Troi in the past timeline talks about her relationship with Riker.
Both the Pasteur and the Enterprise go at speeds exceeding Warp 10, although it has been stated repeatedly that Warp 9 is the maximum. (This was apparently inserted deliberately by the writers, either as an in-joke or to emphasize the whole thing may be a hallucination given to Picard by Q and it's not "really" happening.)
In the past scenes, Data is missing one gold rank pip, making his rank appear to be Lt. Junior Grade. He should be a Lt. Commander (thankfully Picard calls him by his correct rank). (It's interesting to note that Data's rank remained Lt. Commander throughout the entire series, even in all the feature films.)
The question of Data's rank is a bigger goof than that. For some reason, the writers seem to have meant for Data to be a Lieutenant JG (even though we know he was already Lt. Commander by the Farpoint mission). At one point in the past, Picard leaves the bridge to Lt. Yar while Data is sitting right there at Ops. And yet, when Picard meets Data for the first time (again), he DOES call him "Commander Data." So, which is it?
If the rupture is growing backwards in time, the sequence of events shown here is reversed. The future Enterprise crew should see the rupture when they arrive, and then it should get smaller until it vanishes entirely (when they make the scan and create it).
Tomalak says the Romulans will send one of their own ships in to investigate the anomaly along with the Enterprise, but we never see such a ship from then on.
If you look at the command consoles on the captain's chair on the Enterprise from the past, they are moulded into the chair. During the time of the Farpoint mission, the consoles on the chair could be flipped open and closed. The moulded consoles didn't appear until later in the series.
Picard: You accused me of being the representative of a... a barbarous species.
Q: I believe my exact words were "a dangerous, savage, child-race."
Picard: We are who we are. And, we're doing the best that we can.
Q: Humanity's fate has been sealed. You will be destroyed.
Picard: Q, I do not believe even you are capable of such an act.
Q: 'I'? There you go again always blaming me for everything. Well, this time, I'm not your enemy. I'm not the one that causes the annihilation of mankind. You are.
Q: That's right. You're doing it right now. You did it before and you'll do it yet again.
Picard: What sort of meaningless double-talk is this?
Q: He doesn't understand! I have only myself to blame, I suppose. I believed in you. I thought you had potential. May whatever God you believe in have mercy on your souls. This Court stands adjourned.
Deanna: That was an incredible program.
Worf: I am glad you approve. I have always found the Black Sea at night to be a stimulating experience.
Deanna: Worf, we were walking bear foot on the beach with balalaika music in the air, ocean breeze watching over us, stars in the sky, full moon rising, and the most you can say is stimulating?
Worf: It was... very stimulating.
Beverly: I've prepared quarters for you on Deck Five if you'd like some rest.
Picard: I'm fine. I don't need any rest.
Beverly: Nell, please escort the Ambassador to his quarters
Picard: I can find my way around a starship! (addresses the group, and gets mad) You're all treating me like an invalid, but I assure you I've got a few years left. I don't need to be led around and I don't want to be patronized!
Beverly: You're right. I'm sorry...
Picard: (starts for the turbolift) I'll go have a rest.
Picard: Are you responsible for my shifting through time?
Q: I'll answer that question if you promise not to tell anyone (Q gets out of his chair and whispers into Picard's ear) Yes!
Q: Sorry! That's not a yes-or-no question, you forfeit the rest of your questions!
Beverly: Personally, I think that you just like waking everyone up in the middle of the night.
Picard: Actually, I just love roaming the ship in my bare feet.
Q: ( to Picard) That is the exploration that awaits you, not mapping stars or studying nebulae, but charting the unknown possibilties of existence.
Picard: (yelling to the sky) Q! We're here! This has gone on long enough. (to Deanna) Counselor, do you sense an alien presence?
Deanna: No, sir.
Worf: What is a "Q"?
Yar: It's a letter in alphabet as far as I know.
O'Brien: Looks like we'll all be burning the midnight oil on this one.
Data: That would be inadvisable.
O'Brien: Excuse me?
Data: If you attempt to ignite a petroleum product on this ship at zero hundred hours, you will activate the fire suppression system, which would seal off this entire deck.
Data: It appears as though we will be required to ignite the midnight petroleum, Captain.
This episode marks Next Generation as the Star Trek series with the most episodes, beating Deep Space Nine by two.
This episode won an Emmy for Outstanding Individual Achievement in Special Visual Effects.
Both this story and "Encounter at Farpoint" are really considered to be a one-parter (this story being over two hours with the extended scenes included), but both have been converted into a two-part format.
Deleted scenes such as Troi expressing her concern over her and Riker working together to Picard in the Ready Room, in the past timeline were re-incorpated in a special VHS Collector's Edition box set.
When Picard is talking to Riker at Farpoint, the producers get sneaky to make sure Riker "looks" correct (no beard, younger). They use footage of Riker from "The Arsenal of Freedom" - you can see Captain Paul Rice from that episode in the background.
A huge part of the story was written by Michael Piller. He asked not to receive any credit for his work.
The final time, out of a couple of episodes, that we see Picard aged. Others include "Future Imperfect" and "The Inner Light."
Picard keeps calling O'Brien "Chief", a title that he wouldn't hold until much later in the series and Deep Space Nine.
A fourth timeline with the Borg attack from "The Best of Both Worlds" was considered for the story.