This question and answer apply to Minecraft 1.4.7 and earlier. Minecraft 1.5 and later support high-resolution textures automatically, and do not exhibit the misplaced animations described below.
Minecraft versions before 1.5 were not written to support different-resolution textures.
The default Minecraft terrain texture in these versions is a 256×256 image with 16×16 tiles in it (a texture atlas).
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 used by Minecraft 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 recalculating individual pixels and modifying the data of the texture in memory, 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.
The rules of how far fire spreads did not change in 1.6, only how fast. The best guide on fire that I've seen is NZPhoenix's:
Introduction
This thread is currently a basic introduction on the physics of fire in Minecraft. To understand how fire works and spreads, it is important to understand that fire itself is a block. When fire spreads, it doesn't actually spread to a flammable block. Instead, it spreads to an air block next to a flammable block. Only certain air blocks are in range of any given flame, and I call these Flammable Air Blocks(FABs).
Spreading
Fire has an area of Flammable Air Blocks(FABs) to which it can spread. The pattern of FABs is 3x3x6. Fire can spread twice as far vertically as it can horizontally.
As stated later on:
Sadly, fire cannot simply be encased to make it safe, the way lava can be.
The only way to prevent fire from spreading to something is to have all air blocks adjacent it to be out of range of the fire. If you can't, then you have to put another block there. (Another flammable block will do, but you have to block all of it's air spaces too.)
Edit: As for why it suddenly spread now, when it's slower, when it didn't in any prior version, is because shortly after a fire is created, it's ability to spread disappears, even if the fire doesn't. Most people don't notice this because the fire goes out soon anyway, but contrary to rumor, Netherrack can spread fire too, just not for long, and by the time people put flammable stuff by it, its chance is over.
What most likely happened is that, with the newest update, this spreading timer was reset because of the changes that Notch made, and your blocks either weren't there when the fire was started or just didn't catch fire by chance.
Best Answer
Apparently fireballs from lava can tunnel through up to two blocks sometimes causing a considered-to-be-safe location to catch fire.
I had to rebuild my wooden floor three times before I noticed my lava fall outside was to blame. (Since it's SMP with bukkit, WorldGuard solved this issue for me)