Minecraft isn't written to support different-resolution textures.
The default Minecraft terrain texture is a 256×256 image with 16×16 tiles in it.
The code which animates the animated textures in Minecraft (fire, water, lava, and portals) writes onto specific pixel offsets according to 16×16 tiles, which are wrong for larger textures, so you get small fire/water/portal images occupying other blocks. Presumably the patchers replace the 16× factors with 32×, or whatever fits the actual texture resolution.
The reason the textures mostly work is that the OpenGL 3D API mostly takes coordinates in textures in terms of numbers between 0 and 1, rather than 0 and whatever the pixel size of the image is, so the main rendering doesn't care; only the animated textures, which are actually defined in terms of calculating individual pixels, are affected.
Also, tiles over a certain size (128×128, I think) will crash Minecraft. Below that size, you can still use HD textures and it will work except for the misplaced animations. The animated items will not animate, and (for a 32× pack) these will have animations on them: bricks, gold blocks, Netherrack, and pumpkins.