The combination that unlocks Mrs. Packerton's desk is the first four numerals of Pi (3141). You're meant to use the morse code poster and bloodstains next to the lock to find the code for the freezer in the second bedroom of her house, but it's also the same as her desk's password, just backwards. (1413)
This one is also a Fridge Tear Jerker: the exchange between Sal and Dr.Enon at the end of Episode 1 ("I don't think you're a murderer, Sal" - "You might be the only one"). It's not just Dr.Enon being the only one on Sal's side...it's Dr.Enon literally being the only one to consider Sal innocent, because Sal himself doesn't.
Gizmo's antics are not only providing some comic relief - they're, like his name, also shout-outs to the movie. You cannot expose a gremlin to bright lights and water, so what does Gizmo do? Watch TV and take a bath, of course! Now all he has to do for a full set is infiltrate a fridge after midnight.
To get certain achievements, you have to do things outside of the main storyline. They then get referenced in the next episodes in some form - usually as plot points. Thus we can safely assume that things done for achievements outside the main storyline actually happened.note Sleeping aid/laxative choice in Episode 1 is an exception, since you can only get one of them, and laxative is later proven to be the canon option. Why, then, does the game have an achievement for talking to every tenant in Episode 4, the action which doesn't actually move the plot since all you do is talk about mundane stuff, get an occasional sweet moment or two - the furthest things from the main storyline? The answer: to humanize them. To remind both Sal and the player about these characters (or to introduce them, if you managed to avoid meeting them in previous episodes), to evoke empathy, and to make it harder to kill them both in and out of universe.
In one of the optional conversations Mrs. Rosenberg refers to Mr. Addison as a "little boy" and then corrects herself, saying that he probably isn't that little now, it's just the way she sees him. Mrs. Rosenberg is really, really old, so one could easily take her words as reminiscence about the times when Terrence was a kid...however, she is later revealed to be stuck between the worlds of living and dead, while Mr. Addison is revealed to be a ghost of his child self, which means that Mrs. Rosenberg saw him in his true form as that same little boy all this time!
In episode 1, you can choose to knock Charley out with the Addison tea by adding the sleeping pills Sal's father keeps in the bathroom. In episode 2, they are no longer in the bathroom, but in Mr. Fisher's room stuffed behind his desk. It's been confirmed some of the pills in Sal's room are psych meds. Knowing Sal's tragic and mysterious past, his dad hiding his sleeping pills after a bottle of them suddenly goes missing doesn't seem coincidental.
In episodes 1 and 2 you can hear odd noises coming from apartment 201. In episode 3 you find out their source. Word of God says that about two years have passed between episodes 1 and 3. Mrs.Packerton has been dismembering people for two years at least, with no one being the wiser.
Episode 3 has Sal answer "the most popular fan question" by recounting The Bologna Incident. The journalist, Clare Nettles, promises to air the story in full. However, in the past segment of Episode 4 Sal can optionally turn on the TV and see Clare Nettles...who looks nothing like the one who listened to Sal's story. Conclusions? 1) The real Clare was replaced by the cult, 2) The fake Clare was simply gauging how much Sal knows about the cult, and 3) Sal's story will never see the light of day. Also, as pointed out here, there's no red light on the camera (unlike all other cameras in the game), meaning that Sal's interview is not actually being recorded.
Episode 4 when Larry essentially poisons himself with alcohol laced with something to escape Red-Eyes. If Larry hadnt done that, then Sal would have been forced to kill him along with everyone else.
Travis liking bologna sandwiches. At least he (hopefully) never learned what they were made of.