I've been doing a rewatch and making notes of things that are referenced later. Considering most classic Trek has a reputation for being episodic, you'd be surprised just how much gets referenced later, whether in a passing comment or an in-joke or something. The only episodes of TNG season 1 where I didn't spot at least a passing reference later was "Too Short a Season", "Home Soil", and "When the Bough Breaks". (The references to a few of the others are vague and/or arguable though, and admittedly "Knowing where that clip in 'Shades of Gray' is from" qualifies a few of them.)

So it kind of depends on how strictly you define "important." Most people could probably skip almost the entirety of TNG season 1 and not be that confused, but for example:

• "All Good Things..." loses a lot without "Encounter at Farpoint"
• "The Naked Now" is important to "The Measure of a Man"
• "Haven" introduces Lwaxana Troi, Mr. Homn, naked Betazoid weddings, and the running gag of data being too precise. "In the Cradle of Vexilon" loses something without it too.
• "Where No One Has Gone Before" is crucial in introducing the Traveler, and that plot continues into "Remember Me" and "Journey's End" and beyond.
• "The Last Outpost" has first contact with the Ferengi, though you could argue that future Ferengi episodes make more sense without it? Though it's important to the game Star Trek: Resurgence.
• "Justice" doesn't seem important, but if you skip it you won't know what Remmick's talking about in "Conspiracy".
• "The Battle" isn't referenced often, but "Bloodlines" depends on it. Remmick mentions this one too.
• "Hide and Q" introduces concepts like the Q Continuum, and the events of it lead to Q's status in "Q Who", which introduces the Borg.
• "The Big Goodbye" introduces Dixon Hill and explains holodeck matter. The Jarada are mentioned again later too.
• "Datalore" introduces Lore and the Crystalline Entity and explains Data's past, somewhat.
• "11001001" is important to understanding "Future Imperfect"... though that episode isn't really referenced again other than that it introduces a fictionalized version of Nurse Ogawa. So is it still important if you skip both of them?
• "Coming of Age" introduces a lot of the characters and concepts that will be in "Conspiracy". Fun fact: This is the first episode to name Murf's species from Prodigy.
• "Heart of Glory" introduces Khitomer and gives Worf's backstory and sort-of sets up "The Neutral Zone".
• "The Arsenal of Freedom" is the first mention of Crusher's grandmother from "Sub Rosa", but arguably more important for relationship-building between Crusher and Picard.
• "Symbiosis" becomes very relevant in Lower Decks in the episode "Trusted Sources".
• "Skin of Evil" features the death of Tasha Yar. Armus also returns in Lower Decks.
• Even though the cliffhanger isn't followed up on, "Conspiracy" becomes important again in "The Drumhead".
• "The Neutral Zone" pays off the hints that the Romulans were gone, though if you skipped "Heart of Glory" you didn't catch this in the first place, and "Angel One" arguably contradicted it. But this is the first hint of the Borg, as confirmed in "Q Who" and "The Best of Both Worlds".

I could add other subtler things, but those are some of the bigger ones just from that highly-episodic season.