MOTM

>>>>
I noticed that there are two "C25"s on page 2. I imagine that
the one marked "10M" hanging off U8A is the correct one, so what is 
that 0.1M C25 bridging ground and the +15 rail up at the top of the 
page...? I can't seem to identify it by comparing the board to the 
schematic.

(I'm guessing that the numbering is a quirk of the 100/101 revision.)
<<<<

I don't have a 101 schemo, but it would be a labelling mistake to 
have two C25 parts. From your description it sounds like they both 
belong in the circuit though.

>>>>
What *are* those little 'floating' schematic pieces? In the case of 
those floaters in the '101 schematic, are those caps between the 
rails and ground "decoupling capacitors"? Put there to absorb 
fluctuations in current? 
<<<<

Correctimundo.

>>>>
Why aren't they shown where they actually connect in the schematic?
<<<<

Personal preference in schematic drawing style. Some prefer to show 
decoupling caps in place, others prefer to show power supply 
connections and caps in a separate place to make the important parts 
of the circuit plainer.

>>>>
Also, unused portions of op-amps tend to be shown "floating" around, 
too, and connected in weird ways, such as the output connected back 
to the input. Is there a reason for that?
<<<<

Yes. Unused opamps and especially logic gates can affect other opamps 
or gates on the same physical chip. Their state is undefined, and can 
flop around. So you tie logic inputs to ground or V+ (doesn't really 
matter), and you tie opamp inputs to ground, or the output to the 
inverting input as you mentioned. That keeps the state of the unused 
device stable and predictable. Many times it won't make a difference 
in circuit performance, but occasionally it causes problems. It's 
just part of good electrical design that Paul practices.

Moe