Time: This is just a quick paragraph that notes the importance of keeping track of time in the campaign. Like a lot of things in the PHB, it brings up the general concept then passes all responsibility for the specifics on to the Dungeon Master. I assume that there'll be more concrete rules in the DM's Guide.
The most important thing here is the codification of turns, rounds and segments, used to track time during dungeon exploration. A turn is 10 minutes, a melee round is 1 minute, and a segment is 6 seconds. Again this isn't explained further here, but I wanted to bring it up because the terminology was pretty loose in OD&D: turns and rounds were tossed out interchangeably. From this point on, the game tightens up on this kind of thing.
Distance: The main thrust of this section is the rule that ranges for missiles and spells are effectively tripled when aboveground. Every ranged attack in the game has a value denoted with the " symbol - when underground it represents 10 feet, and when aboveground it represents 10 yards. The rule is intended to simulate the idea that you can fire arrows and such further without the impediment of a roof, and the darkness of the dungeon.. Works for me.
It's important to note that this conversion is only done for range, and not for area of effect. It's so important that Gary writes a whole sentence in ALL CAPS. Basically, a fireball shouldn't triple in size just because you're outside.
Monster, The Term: Possibly the most pointless section of the book, in which Gary notes that the term monster is used to describe pretty much any creature you can encounter. I guess some people need to be told that not all monsters are evil? Ah well, it's not like it takes up much space.
Character Spells: And now we reach the section I've been dreading the most: the spell list. I'm not going to start on that today, but I'll do the preliminary stuff.
The most interesting tidbit here comes in the description of how cleric spells function. Clerics have to pray for their spells (in advance, of course). Spells of 1st through 4th level are granted to the cleric by lesser servant of the cleric's deity, and it seems like there's not much limit on those. Higher level spells, however, can only be granted by the deity directly, and this is subject to all sorts of factors. The door is opened here for the DM to require that a cleric makes sacrifices and atonements for high level spells, which could get really annoying. I'd be inclined to ignore this except in extreme circumstances, such as a severe alignment deviation.
There's not much that's new in the section on magic-users. It's the same standard, Vancian system from OD&D, which is fine by me. D&D just ain't D&D without it.