Spikes was on Koga's Forretress so if you don't OHKO it, then you will likely see it. (very possible considering the rarity of Fire Types in GSC)Just thought of another couple of examples: Spikes. Despite being introduced in Gen II, only Pineco and Forretress learn it in GS, relatively late at 43 and 49 respectively. Nothing learns it by breeding; Cloyster gets it at Level 33, but only in Crystal. Qwilfish (which gets it at level 1 in Crystal, but not GS) can be caught at Level 15 during a Swarm, but still won't have it as Tackle, Poison Sting, Harden, and Minimize all come before Spikes in its moveset. The only opponent which has it is Koga's Forretress, so it's very easy to miss. Gen III made it somewhat more widespread, with Cacnea, Skarmory, and Deoxys-D all getting it, as well as Omanyte and Snorunt via breeding.
The second is Spark, which for ages I was convinced was introduced in Gen III instead of II. If you never used Raikou after catching it, you'll miss it; the only other Pokemon to get it are Chinchou or Lanturn, which no opponent uses and won't know the move when caught (Chinchou in Olivine City are caught at Level 20, while Lanturn can typically only be caught at Level 40 using the Super Rod; both Pokemon learn it at Level 25). Gen III makes it far more widespread; practically every Electric-type gets it as an early move at some point (you'll see it in Wattson and Surge's gyms). And Barboach gets it via breeding... an odd choice, unless there's some flavour-related reason I'm not aware of.
I agree with you about Spark since the only reason I know it exists is because I use the Fishing Rod everywhere.
I was convinced that Mach Punch was introduced in Gen 3. Turns out it was a Gen 2 move learned by Hitmonchan. The only way to get Hitmonchan is through a tedious side quest for Tyrougue and is not reliable.