Play Rough, Sleep Powder, Megahorn, Earth Power has no new old species learning it.
Moonblast is now learnt by Hoothoot, Noctowl.
Hurricane is now learnt by Gyarados, Taillow, Swellow.
Crunch is now learnt by Bidoof, Bibarel.
Nasty Plot is now learnt by Patrat, Watchog.
Night Daze, Aromatic Mist are no longer signature moves.
Edit: All Wormadam Formes now get Quiver Dance, Bug Buzz and Sucker Punch.
Edit 2: Surskit, Masquerain, Mothim get Lunge.
Bellossom gets Quiver Dance.
Edit 3: Dunsparce gets Dragon Rush and Air Slash. Taillow and Swellow get Reversal.
Edit 4: Simis get Starter Tutors. Pledges are exclusive to their evolutions, while H-Beam variants are now obtained through Tutor. This is likely an error on Kaphotics' part, as Simis don't get Pledges, so it is likely supposed to be the reverse(ie. Monkeys now get Pledges).
Edit 5: Castform gets Cosmic Power.
Edit 6: Sudowoodo gets Head Smash, but not Bonsly.
Edit 7: Pichu-line now gets Electric Terrain.
Edit 8: Zapdos gets Magnetic Flux, Moltres gets Burn Up. Growlithe-line and Cyndaquil-line get Burn Up.
Edit 9: Toxic Thread is exclusive to Spinarak-line.
Edit 10: Sandile-line, Mankey-line, Pancham-line get Power Trip. Golduck gets Me First. Mankey, Golett, Cubone-lines get Stomping Tantrum.
Edit 11: Mewtwo and Lucario get Laser Focus. Musharna and Beheeyem get Psychic Terrain. Luvdisc gets Heart Stamp. Snorlax and Golurk get High Horsepower. Corsola and Tirtouga-lines get Liquidation.
Edit 12: Carvanha-line and Lillipup-line get Psychic Fangs.
Edit 13: Doduo-line gets Swords Dance and Jump Kick. There are no new old species that get Brave Bird.
Edit 14: Bonsly-line gets Tearful Look. Zip Zap is exclusive to Togedemaru. Shadow Bone is exclusive to Alolan Marowak. Heatmor and Litleo-line get Flare Blitz. Beak Blast is exclusive to Toucannon. Instruct is exclusive to Oranguru. Trop Kick is exclusive to Tsareena. Purify is exclusive to Pyukumuku. Nidorino, Nidoking, Nidorina, Nidoqueen, Rapidash, Seel, Dewgong, Cloyster, Rhyhorn, Rhydon, Rhyperior, Goldeen, Seaking, Tauros, Lapras, Mew, Ariados, Togetic, Togekiss, Aggron, Samurott, Excadrill, Scolipede, Escavalier, Bouffalant, Thundurus, get Smart Strike through TM.
Edit 15: Emolga and Alolan Raichu get Speed Swap. Fire Lash is exclusive to Heatmor. Anchor Shot is exclusive to Dhelmise. Klinklang gets Gear Up. Clefairy, Clefable, Spinda, Starmie get Spotlight. Solar Blade is exclusive to Lurantis. Machamp gets Strength through Level-Up, becoming the only species to get it. Floral Healing is exclusive to Comfey. Baneful Bunker is exclusive to Toxapex. Shore Up is exclusive to Sandygast-line. First Impression is exclusive to Golisopod.
Edit 16: Way too many species get Brutal Swing. Jynx, Articuno, Smoochum, Mew, Delibird, Cryogonal, Regice, Glaceon, Froslass, Alolan Sandshrew-line and Alolan Vulpix-line get Aurora Veil. Eeveelutions and Lopunny get Baby-Doll Eyes in their Level-Up movesets. Sneasel-Weavile and Incineroar get Throat Chop.
Edit 17: Leech Life is NOT learned by old species besides the current ones. Alolan Sandshrew gets it, however.
Yanma-line retains it through Egg Move, so does Bellsprout-line. Yanma also gets it through TM, while Bellsprout gets it exclusively from Egg Move.
Edit 18: Rock Wrecker, Poison Tail, Poison Fang, Poison Gas are not learned by anyone new. Tail Slap's only new learner is Alolan Vulpix-line besides the current learners. Furret gets Coil. Ariados gets Swords Dance. Swalot gets Venom Drench at start. Wailord gets Noble Roar. and Soak at start. Camerupt no longer gets Rock Slide at Level 33, instead it gets it at start. Grumpig gets Belch. Vibrava now gets Dragon Breath at start. Flygon gets Dragon Dance and Dragon Claw at start alongside Dragon Breath.
Edit 19: Altaria gets Dragon Breath at start, not level up. Lunatone gets Power Gem and Psyshock at start, Solrock gets Flare Blitz. Whiscash gets Thrash and Belch. Crawdaunt no longer gets Swift at evolution, but at start. Claydol no longer gets Hyper Beam at Level Up, but at start. Anorith-line's movepool have been fixed. Milotic now gets Water Pulse at start, not through Level-Up. Dusclops now gets Shadow Punch at start, not through Level-Up. Glalie no longer gets Freeze-Dry through Level-Up, but gets it at start. Sealeo no longer gets Swagger through level-up, neither does Walrein for Ice Fang. They are both at start. Shelgon and Salamence now get their exclusive Level-Up moves, Protect, Fly, Dragon Tail, Elemental Fangs at start. Metagross gets Hammer Arm similarly at start, whereas Metang no longer gets Confusion through Level-Up.
It seems this part continues on to other species.
Edit 20: Ambipom gets Dual Chop. Probopass gets Tri Attack. Throh gets Mat Block. Alomomola gets Play Nice. Pangoro gets Bullet Punch.