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1. Types:
All moves of the following are PHYSICAL: Normal, Fighting, Ghost, Poison, Rock, Ground, Steel, Bug, Flying (example: Shadow Ball, 	Sludge Bomb, Hyper Voice)
All moves of the following are SPECIAL: Dark, Dragon, Fire, Ice, Water, Grass, Electric, Psychic (example: Crunch, Dragon Claw, Fire Punch)
Steel resists Dark and Ghost. There are no Fairy types.

2. Items:
There is no Choice Specs, Choice Scarf, Life Orb, Expert Belt, Super Effective reducing berries, Assault Vest, Eviolite, Rocky Helmet, Weakness Policy, etc; Sitrus Berry only heals 30 HP instead of 1/4 of the total HP.
More common and effective items include: Choice Band, Leftovers, Lum Berry, Pinch berries. It is generally recommended to NOT use items like Silk Scarf, Magnet, Mystic Water, etc unless for specific cases or if a Pokemon would be better off not holding one of the items above.

3. Abilities:
No hidden abilities.
Sturdy only protects against OHKO moves like Sheer Cold, Fissure, etc. 
Flash Fire is not activated by Will-O-Wisp.
Oblivious does not prevent Taunt.
If a user has Guts and is burned, burn's effect of lowering Attack is not applied. Otherwise, if a user does not have Guts and is burned, burn's effect is applied. In combination with Facade, even if the user is burned, if the user does not have Guts, the user will not recieve the attack boost.

4. Status:
You can paralyze Electric types with Thunder Wave and put to sleep Grass types with Spore or Sleep Powder.
Sleep turns last 2 to 5 turns.
Burning sleep turns (from Rest) is a bit funky in ADV. See this post for details.
To burn sleep turns by using Rest and you don't switch out during the process, simply stay in and use Sleep Talk or stay asleep for 2 turns. You will wake up on the 3rd turn.
If you use Sleep Talk for 2 turns, then switch out, then switch back in the sleeping Pokemon, you will have to stay asleep for 2 more turns, meaning you have to Sleep Talk for 2 more turns (the counter stays at 0).
If you use Sleep Talk for 1 turn, then switch out, then come back in, use Sleep Talk, then switch out, then come back in, repeatedly, you will stay asleep the entire time because Sleep Talk does not burn Sleep turns in this case. (this is similar to the point above)
If you use Sleep Talk for 1 turn, then DON'T use Sleep Talk the next turn, then you switch out, the counter does not reset in this case, and you will wake up the next time you switch in. 
If you don't use Sleep Talk for 1 turn (you have now successfully burned 1 turn of sleep and increased the counter), then DO use Sleep Talk the next turn (the counter doesn't change here), then switch out, then switch back in, you will still need to burn 1 more turn of sleep before waking up.
Since sleep turns don't reset, if you don't use Sleep Talk for 1 turn while asleep (the counter increases by 1), then switch out, then switch back in, you will also need to burn 1 more of turn of sleep before waking up, just like the above point.
Simply put: Staying in and burning sleep turns is as normal. However if asleep and you click Sleep Talk for x amount of turns, then switch out before waking up, those x amount of turns you spent clicking Sleep Talk will be back to 0 (plus the turns you didn't click Sleep Talk). (EXCEPT for point IV) 

5. Moves:
Hidden Powers can be Physical or Special; they are 70 base power instead of 60.
Taunt lasts 2 turns only (including the turn you used it on), while Encore lasts 2 to 5 turns.
Wish is not dependent on the user's HP; it always restores 50% health.
Explosion halves the physical defense of the opponent, although it is listed as 500 BP.
There is no U-Turn or Volt Switch for momentum; only Baton Pass.
Will-O-Wisp has 75 accuracy, instead of the current 85. Toxic has 85 accuracy, instead of the current 90. Hypnosis is 60 accuracy; Disable is 55 accuracy. Giga Drain is only 8 PP.
Knock Off is a special Dark attack, and is only base 20 power; it is used for utility instead of damage.
High Jump Kick does not take crash recoil if used against a Ghost type.
Quick Attack, Fake Out, Extreme Speed and Mach Punch are the only forms of priority (Extreme Speed is also +1 in Gen 3).

6. Gameplay:
You lead with the Pokemon that's in the first slot of the teambuilder. There is no team preview, so you cannot pick your lead beyond placing a Pokemon in the first slot of the teambuilder beforehand.
Critical hits deal double damage this generation, instead of the current 1.5x multiplier. Critical hits ignore the user's negative stat changes, the opponent's positive stat changes, screens, but not the effect of burn.
Leftovers and other residual damage activate after a new Pokemon is brought in following a KO of the previous Pokemon. (KO -> New Pokemon Brought In -> Residuals)
After fainting to a self induced recoil move, the opponent, if slower, will not make a move. As a catch all rule, the end of a turn is declared the moment a Pokemon faints.