I've never heard of collision detection being incorrect for the classic graphics and I'd think it'd be impossible just because of how the Blam engine works. If I'm not mistaken, the Halo level geometry is the level geometry and there is only one version of it. In modern games there are often multiple meshes (some render and some are just for calculations,) but Halo came out on the tail end of the 2nd gen of 3d games, and I tend to group it with Quake and Unreal, at least in terms of their engines. You may be mistaken because of minor differences between what's shown to you and what the game is calculating. Your weapon is not in the game world, it's a special model that is shown only on your hud. The weapon that you really have is the one your character model is holding, and it's muzzle may not be in exactly the same place as where you think it is. You mentioned corners, this is the most obvious spot this happens. There have been plenty of times where I'm trying to shoot a rocket around a corner. I can see the target, recital is red, and you pull the trigger only for the rocket to blow up on the wall next to you.
There was probably different levels of care paid to each mission just because designers get tired out, take shortcuts, or just plain miss things. For me, 15 minutes into any speedrun of The Library, my viewers always see me do this:
While it may look like it, I'm not out of bounds, I'm just tucked myself into a little corner where the new geometry goes so far over the original that you can walk through it. The Library is actually notorious for this as it's not the only place you can do this (it's just the only place that's useful in a speedrun.) There's actually an entire room right at the end of The Library that has a rocket launcher in it. There is a false wall over it so in anniversary, you wouldn't ever know it's there unless you happened to walk through the wall or know it's there from classic.