Mew can't learn certain moves such as Hydro Cannon, what are the other moves Mew cannot learn?
I'm working on a full list of all of Mew's impossible moves. Some of the moves I've included are only possible in a previous generation, but since transferring it over to a new game is possible it is 100% possible to have those moves.
-Absorb -Acid -Acid Armour -Acid Spray -Acupressure -Aeroblast -Agility -Air Cutter (but possible in gen 4 via move tutor) -Air Slash -Ally Switch (but possible in gen 5 via tm) -Aqua Jet -Aqua Ring -Arm Thrust -Aromatherapy -Aromatic Mist -Assist -Assurance -Astonish -Attack Order -Aurora Beam -Autotomize -Avalanche (but possible in gen 4 via tm) -Baby-Doll Eyes -Barrage -Beat Up -Belch -Belly Drum -Bestow -Bide -Bite -Blast Burn -Blaze Kick -Blue Flare -Body Slam (but possible in gen 3 via move tutor) -Bolt Strike -Bone Club -Bone Rush -Boomerang -Boom Burst -Brave Bird -Brine (but possible in gen 4 via tm) -Bubble -Bubble Beam -Bug Buzz -Bullet Punch -Bullet Seed (but possible in gen 4 via tm) -Camouflage -Captivate (but possible in gen 4 via tm) -Celebrate -Charge -Charm -Chatter -Chip Away -Circle Throw -Clamp -Clear Smog -Close Combat -Coil -Comet Punch -Confuse Ray -Confusion -Constrict -Conversion -Conversion 2 -Copycat -Cosmic Power -Cotton Guard -Cotton Spore -Counter (but possible in gen 3 via move tutor) -Crabhammer -Crafty Shield -Cross Chop -Cross Poison -Crunch -Crush Claw -Crush Grip -Curse -Dark Void -Defend Order -Defence Curl (but possible in gen 3 via move tutor) -Defog (but possible in gen 4 via tm) -Destiny Bond -Detect -Diamond Storm -Disable -Disarming Voice -Discharge -Dizzy Punch -Doom Desire -Double Hit -Double Kick -Double Slap -Double-Edge (but possible in gen 3 via move tutor) -Draco Meteor -Dragon Ascent -Dragon Breath -Dragon Dance -Dragon Rage -Dragon Rush -Draining Kiss -Drill Peck -Dynamic Punch (but possible in gen 3 via move muter) -Eerie Impulse -Egg Bomb -Electric Terrain -Electrify -Electro Ball -Ember -Encore -Entrainment -Eruption -Extrasensory -Extreme Speed -Fairy Lock -Fairy Wind -Fake Tears -Feather Dance -Feint -Fell Stinger -Fiery Dance -Final Gambit -Fire Fang -Fire Pledge -Fire Spin -Fissure -Flail -Flame Burst -Flame Wheel -Flare Blitz -Flatter -Flower Shield -Flying Press -Focus Energy -Follow Me -Force Palm -Foresight -Forest's Curse -Freeze Shock -Freeze Dry -Frenzy Plant -Fury Attack -Fury Cutter (but possible in gen 4 via move tutor) -Fury Swipes -Fusion Bolt -Fusion Flare -Future Sight -Gear Grind -Geomancy -Glaciate -Glare -Grass Pledge -Grass Whistle -Grassy Terrain -Gravity -Growl -Growth -Grudge -Guard Split -Guard Swap -Guillotine -Gust -Hammer Arm -Happy Hour -Harden -Haze -Head Charge -Head Smash -Headbutt (but possible in gen 4 via move tutor) -Heal Block -Heal Order -Heal Pulse -Healing Wish -Heart Stamp -Heart Swap -Heat Crash -Heavy Slam -Hex -High Jump Kick -Hold Back -Hold Hands -Horn Attack -Horn Drill -Horn Leech -Howl -Hurricane -Hydro Cannon -Hydro Pump -Hyper Fang -Hyperspace Fury -Hyperspace Hole -Ice Ball -Ice Burn -Ice Fang -Ice Shard -Icicle Crash -Icicle Spear -Imprison -Inferno -Ingrain -Ion Deluge -Judgment -Jump Kick -Karate Chop -Kinesis -King's Shield -Knock Off -Land's Wrath -Lava Plume -Leaf Blade -Leaf Storm -Leaf Tornado -Leech Life -Leech Seed -Leer -Lick -Light Of Ruin -Lock on -Lovely Kiss -Lucky Chant -Lunar Dance -Luster Purge -Mach Punch -Magical Leaf -Magma Storm -Magnet Bomb -Magnetic Flux -Magnitude -Mat Block -Mean Look -Meditate -Mega Drain -Mega Kick (but possible in gen 3 via move tutor) -Mega Horn -Memento -Metal Burst -Metal Claw -Metal Sound -Meteor Mash -Milk Drink -Mimic (but possible in gen 3 via move tutor) -Mind Reader -Minimize -Miracle Eye -Mirror Coat -Mirror Move -Mirror Shot -Mist -Mist Ball -Misty Terrain -Moonblast -Moonlight -Morning Sun -Mud Bomb -Mud Shot -Mud Sport -Mud Slap (but possible in gen 4 via move tutor) -Muddy Water -Mystical Fire -Natural Gift (but possible in gen 4 via tm) -Needle Arm -Night Wave -Night Slash -Noble Roar -Nuzzle -Oblivion Wing -Octazooka -Odour Sleuth -Ominous Wind (but possible in gen 4 via move tutor) -Origin Pulse -Outrage -Parabolic Charge -Parting Shot -Pay Day -Peck -Perish Song -Petal Blizzard -Petal Dance -Phantom Force -Pin Missile -Play Nice -Play Rough -Pluck (but possible in gen 5 via tm) -Poison Fang -Poison Gas -Poison Tail -Powder -Powder Snow -Power Gem -Power Split -Power Swap -Power Whip -Precipice Blades -Present -Psybeam -Psycho Boost -Psycho Cut -Psycho Shift -Psystrike -Psywave -Punishment -Pursuit -Qucik Attack -Quick Guard -Quiver Dance -Rage -Rage Powder -Rapid Spin -Razor Leaf -Razor Shell -Razor Wind -Recover -Refresh -Relic Song -Revenge -Reversal -Roar Of Time -Rock Blast -Rock Climb (but possible in gen 4 via hm) -Rock Throw -Rock Wrecker -Rolling Kick -Rollout (but possible in gen 4 via move tutor) -Rototiller -Sacred Fire -Sacred Sword -Sand Attack -Sand Tomb -Scary Face -Scratch -Screech -Searing Shot -Secret Sword -Seed Flare -Seismic Toss (but possible in gen 3 via move tutor) -Self-Destruct -Shadow Force -Shadow Punch -Shadow Sneak -Sharpen -Sheer Cold -Shell Smash -Shift Gear -Silver Wind (but possible in gen 4 via tm) -Simple Beam -Sing -Sketch -Sky Uppercut -Slack Off -Slam -Slash -Sleep Powder -Sludge -Smelling Salts -Smog -Smokescreen -Soak -Sonic Boom -Spacial Rend -Spark -Spider Web -Spike Cannon -Spikes -Spikey Shield -Spit Up -Spore -Steam Eruption -Steamroller -Sticky Web -Stockpile -Stomp -Stored Power -Storm Throw -String Shot (but possible in gen 4 via move tutor) -Struggle (this move can only be used if the PP of all other moves are gone. There is no way to actually have it learnt as a true move, however) -Stun Spore -Submission -Sucker Punch (but possible in gen 4 via move tutor) -Supersonic -Swallow -Sweet Kiss -Sweet Scent -Swift (but posible in gen 4 via move tutor) -Sweet Scent -Switcheroo -Synchronize -Tackle -Tail Glow -Tail Slap -Tail Whip -Take Down -Techno Blast -Teeter Dance -Telekinesis (but possible in gen 5 via move tutor) -Teleport -Thousand Arrows -Thousand Waves -Thrash -Thunder Shock -Tickle -Topsy-Turvy -Toxic Spikes -Tri Attack -Trick-Or-Treat -Triple Kick -Trump Card -Twineedle -Twister (but possible on gen 4 via move tutor) -V-Create -Vaccuum Wave (but possible in gen 4 via move tutor) -Venom Drench -Vice Grip -Vine Whip -Vital Throw -Volt Tackle -Wake-Up-Slap -Water Gun -Water Pledge -Water Shuriken -Water Sport -Water Sprout -Weather Ball -Whirlpool (but possible in gen 4 via hm) -Whirlwind -Wide Guard -Wing Attack -Wish -Withdraw -Wood Hammer -Work Up (but possible in gen 5 via tm) -Wrap -Wring Out -Yawn
Source. Looked through the list at every move to check if Mew can learn it.