I noticed some mistakes with regard to Move Tutor moves.
Note: when I say that a Pokemon can or can't learn a move, I only mean with regard to learning it from a Move Tutor.
http://www.serebii.net/attackdex-dp/aircutter.shtml
Aerodactyl can learn Air Cutter.
http://www.serebii.net/attackdex-dp/furycutter.shtml
Nidoqueen, Nidoking, and Mamoswine can learn Fury Cutter.
http://www.serebii.net/attackdex-dp/icepunch.shtml
Slowpoke can't learn Ice Punch.
http://www.serebii.net/attackdex-dp/icywind.shtml
Slowpoke, Sneasel, and Swinub can learn Icy Wind.
http://www.serebii.net/attackdex-dp/knockoff.shtml
Machop, Machoke, and Machamp can't learn Knock Off. Lickitung, Gligar, Skorupi, Weavile, and Mamoswine can learn Knock Off.
http://www.serebii.net/attackdex-dp/suckerpunch.shtml
Kangaskhan, Celebi, and Duskull can learn Sucker Punch.
http://www.serebii.net/attackdex-dp/trick.shtml
Duskull can learn Trick.
http://www.serebii.net/attackdex-dp/helpinghand.shtml
Nidoran(F), Poliwag, Poliwhirl, and Eevee can learn Helping Hand.
http://www.serebii.net/attackdex-dp/lastresort.shtml
Phanpy can't learn Last Resort. Chingling can learn Last Resort.
http://www.serebii.net/attackdex-dp/snore.shtml
Aerodactyl can learn Snore.
http://www.serebii.net/attackdex-dp/swift.shtml
Aerodactyl, Cyndaquil, Quilava, and Uxie can learn Swift.
http://www.serebii.net/attackdex-dp/uproar.shtml
Roserade can't learn Uproar. Meowth, Exeggcute, Tauros, Hoothoot, Yanma, Swablu, Altaria, and Chingling can learn Uproar.
http://www.serebii.net/attackdex-dp/ancientpower.shtml
Togepi, Lileep, and Jirachi can learn AncientPower.
http://www.serebii.net/attackdex-dp/bounce.shtml
Donphan can learn Bounce.
http://www.serebii.net/attackdex-dp/earthpower.shtml
Sunflora (and possibly Sunkern) can learn Earth Power in HG/SS.
http://www.serebii.net/attackdex-dp/endeavor.shtml
Phanpy and Donphan can learn Endeavor.
http://www.serebii.net/attackdex-dp/gunkshot.shtml
Chimchar and Monferno can learn Gunk Shot.
http://www.serebii.net/attackdex-dp/irondefense.shtml
Solrock can learn Iron Defense.
http://www.serebii.net/attackdex-dp/mud-slap.shtml
Weezing, Omastar, Ledian, and Qwilfish can't learn Mud-Slap. Shuckle, Larvitar, Pupitar, Phione, and Manaphy can learn Mud-Slap.
http://www.serebii.net/attackdex-dp/outrage.shtml
Munchlax can't learn Outrage. Rhydon can learn Outrage.
http://www.serebii.net/attackdex-dp/rollout.shtml
Weezing, Omastar, Ledian, Qwilfish, Shuckle, Azurill, and Wormadam (Sandy Cloak only) can learn Rollout.
http://www.serebii.net/attackdex-dp/signalbeam.shtml
Wigglytuff can't learn Signal Beam.
http://www.serebii.net/attackdex-dp/superpower.shtml
Totodile, Turtwig, Grotle, and Munchlax can learn Superpower.
http://www.serebii.net/attackdex-dp/twister.shtml
Togetic and Togekiss can learn Twister.
With special regard to the two forms of Giratina:
http://www.serebii.net/attackdex-dp/aircutter.shtml
http://www.serebii.net/attackdex-dp/furycutter.shtml
http://www.serebii.net/attackdex-dp/icywind.shtml
http://www.serebii.net/attackdex-dp/ominouswind.shtml
http://www.serebii.net/attackdex-dp/snore.shtml
http://www.serebii.net/attackdex-dp/spite.shtml
http://www.serebii.net/attackdex-dp/swift.shtml
http://www.serebii.net/attackdex-dp/ancientpower.shtml
http://www.serebii.net/attackdex-dp/aquatail.shtml
http://www.serebii.net/attackdex-dp/earthpower.shtml
http://www.serebii.net/attackdex-dp/ironhead.shtml
http://www.serebii.net/attackdex-dp/outrage.shtml
http://www.serebii.net/attackdex-dp/mud-slap.shtml
http://www.serebii.net/attackdex-dp/twister.shtml
http://www.serebii.net/attackdex-dp/headbutt.shtml
http://www.serebii.net/attackdex-dp/gravity.shtml
Giratina can learn Air Cutter, Fury Cutter, Icy Wind, Ominous Wind, Snore, Spite, Swift, AncientPower, Aqua Tail, Earth Power, Iron Head, Outrage, Mud-Slap, Twister, Headbutt, and Gravity in both of its forms.
http://www.serebii.net/attackdex-dp/magiccoat.shtml
http://www.serebii.net/attackdex-dp/tailwind.shtml
Giratina can only learn Magic Coat when in the Origin Form.
http://www.serebii.net/attackdex-dp/roleplay.shtml
Giratina can't learn Role Play.
With special regard to the six forms of Rotom:
http://www.serebii.net/attackdex-dp/ominouswind.shtml
http://www.serebii.net/attackdex-dp/suckerpunch.shtml
http://www.serebii.net/attackdex-dp/trick.shtml
http://www.serebii.net/attackdex-dp/snore.shtml
http://www.serebii.net/attackdex-dp/spite.shtml
http://www.serebii.net/attackdex-dp/swift.shtml
http://www.serebii.net/attackdex-dp/uproar.shtml
http://www.serebii.net/attackdex-dp/mud-slap.shtml
http://www.serebii.net/attackdex-dp/signalbeam.shtml
http://www.serebii.net/attackdex-dp/painsplit.shtml
The level displays for the machine forms of Rotom look strange (well, for the moves that Rotom learns by leveling up). Also, Rotom can learn Ominous Wind, Sucker Punch, Trick, Snore, Spite, Swift, Uproar, Mud-Slap, Signal Beam, and Pain Split in all of its forms.