GSC Quirks

Gengar
Abilities do not exist (Gengar can be hit with Earthquake).
Natures do not exist.
Choice items, Eviolite, stat-boosting berries, and resist berries do not exist.
Berries have different names (Lum is called Miracle Berry, Chesto is called Mint Berry).
Items that slightly boost the power of a type of move (Miracle Seed, Charcoal, Twisted Spoon), boost by 1.1x instead of 1.2x.

Umbreon
All EVs can be maxed out at once (252/252/252/252/252/252).
Uses "DVs" instead of IVs, which cap at 15 instead of 31 but otherwise work the same way.
Speed DVs can be lowered to break speed ties (Umbreon, Misdreavous).
Pokemon being Shiny requires reduced DVs.
The gender of a Pokemon is determined by its DVs. Aside from female-only Pokemon like Miltank and Blissey, the formula used results in any Pokemon with max DVs being male.

Marowak
Boosting moves only continue raising a stat until the cap of 999 is reached, at which point they will stop increasing.
The exception is Marowak, with an attack stat so high thanks to Thick Club that one SD will send it past the attack cap, past 1024 and wraps back around to a low number.
This is the reason for the special DVs on the Marowak sets in the compendium - it allows Marowak to use SD once without breaking this cap.
The maximum PP of a move that begins at 40 PP (Growl) is 61.
Recoil damage including Struggle is a 1/4 of the damage you deal with the move.
Crash damage from missing High Jump Kick is only 1/8 the damage it would have dealt.

Ursaring
Critical hit damage doubles the Pokemon's level in the calculation, not the damage dealt.
Crits also ignore stat modifiers, burn damage reduction, and screens, if the target's defense stat stage is greater than or equal to the attacker's attacking stat stage.
(This means a crit at +2 against a +2 mon does the same as a +1 crit on against a +2 mon, the damage only goes up if it was +3 or greater against +2).
End of turn effects (poison, leech seed, leftovers) apply when a Pokemon is done with its attack, potentially in the middle of a turn.
Sandstorm does 1/8th max HP per turn instead of 1/16th.
Moves with guaranteed secondary effects (Icy Wind, Thief), have a 1/256 chance to not have that secondary effect trigger.

Venusaur
Growth is the only Special Attack boosting move. Growth's effect is unchanged in harsh sunlight.
Substitute is not available for most Johto Pokemon because it was a TM in gen 1 but not gen 2.
Protect fails when used behind a Substitute.
Absorbing moves like Giga Drain, Mega Drain, Leech Seed, Absorb, and Leech Life fail against Substitute.
You can successfully Sleep Talk Rest while asleep, which will restore your health and reset sleep turns.
Moves called by other moves (Sleep Talk) cannot be Countered or Mirror Coated.

Mr. Mime
Encore lasts 3-6 turns.
Disable has 55% accuracy and lasts 1-7 turns.
Low Kick is not based on weight. Instead, it's a 50 BP Fighting move with 90% accuracy and a 30% chance to flinch.
Conversion2 is blocked by Protect.
Belly Drum boosts attack by 2 when it fails.