Before I go on, I feel the need to point out that Holmes Basic is the first D&D rule set to have a monster’s stats grouped together with its description. God bless functional design!
Gnome: In OD&D, gnomes could be Lawful or Neutral. Here, they are either Neutral or Chaotic Good. There’s a note at the end that Gnomes favour crossbows, which is something that’s never been brought up before, and doesn’t stick around in the future so far as I recall. I'm going to play it up, though. It does fit well with the 'tinker gnome' theme that crept into the race in the late 80s.
Goblin: In OD&D goblins all carried 1-6 gold pieces each. Now they carry 2-12 electrum pieces, which is the exact same value expressed in different coinage. Their alignment has changed from Chaotic to Lawful Evil. In Supplement I their standard damage was set at 1-4, but here it’s been upped to 1-6. The only other difference noted is that the Goblin King and his bodyguards don’t suffer the -1 penalty in daylight, but OD&D’s assertion that they fight as hobgoblins may have been intended to cover that.
Gray Ooze: These are exactly the same as in OD&D. The only minor difference is that it isn’t noted that gray oozes can’t dissolve wood or stone. And the psionic powers from Supplement III don’t make it either, but then again psionics aren’t present in Holmes at all.
Green Slime: Just as in OD&D, with an additional note that green slime often drops from the ceiling onto unwary adventurer. A welcome addition!
Griffon: For some reason, their Armor Class has changed from 3 to 5. They also now get a physical description, though a rudimentary knowledge of mythology would have provided that already
Harpy: The harpy’s damage range has changed, as they now do 1-4 with each attack instead of 1-3 per claw and 1-6 with a weapon. Seems reasonable, as the image of weapon-wielding harpies doesn't really sit right. They have also changed from Chaotic to Chaotic Evil. Otherwise, they’re just as in OD&D.
Hell Hound: Their alignment has changed from Chaotic to Lawful Evil. Holmes has house-ruled the breath weapon, saying that it requires an attack roll on the regular combat chart for monsters. Their supposed great stealth isn’t mentioned, nor is their tendency to hang around with fire giants.
Hippogriff: They now have an alignment of Neutral.
Hobgoblin: Their Armor Class has changed from 5 to 6; I suppose they have downgraded from chainmail to leather and shield? Although their movement rate remains unchanged... Their alignment was previously Chaotic, but now they are Lawful Evil. Otherwise they’re just like in OD&D.
Horse: Just as in OD&D.
Hydra: Just as in OD&D.
Kobold: Individual treasures for kobolds have been lessened from 1-6 gold pieces each to 3-24 copper pieces. Looks like the kobolds of the world have fallen on hard times! Their alignment has changed from Chaotic to Lawful Evil. It’s weird that kobolds are generally said to be weaker than goblins, but a kobold chieftain (who fights as a gnoll) is stronger than a goblin king (who fights as a hobgoblin). They are also described as dwarf-like, very much unlike the canine appearance they had already been given in earlier products, as well as the upcoming Monster Manual. I'm going to chalk that up to a reference to their size, rather than their appearance. Finally, they get a +3 bonus to saving throws that is unique to Holmes so far as I know. It seems he was really embracing that whole ‘dwarf-like’ thing.