First things first. None of this stuff has anything to do with Hijack. The menu order of the player software is not controlled by hijack.

I see the logic for Shuffle: "Off is always selected so you can always switch it off"

Not exactly. Off is the default selection if one of the shuffle modes is activated. If shuffle is off, and you select the Shuffle menu, it shows you the last shuffle mode. Reason: FAQ entry here.

Interesting point about how the positioning of the items themselves within the menu seems to change around a bit. Not sure why that is. Never bothered me...

but that's not consistent with Info

Insert Walt Whitman quote here.

In any case, I don't think the behavior of the menus has changed between 2.0 beta 13 and 2.0 final. Didn't you notice this happening in beta 13? Why wait until now to complain? They even did a "last call for beta 13 bugs" shortly before their last pizza session.

If I'm viewing in Line mode and I enter the Info menu, it has Now&Next selected. Then, if I select Now & Next, when I enter the Info menu, it has Transient selected. Why is this?

I'd guess because it allows you to cycle through the info modes easily, from the front panel, without using the remote control.

Then I won't even ask what is the function of holding the Down button at the playing view because I can just look that up in the documentation (though I'd have to look up where to find the documentation). All I know is it doesn't turn Info on and off and it doesn't go to the previous Info mode, so I don't know.

Holding the Down button toggles between the last screen which showed some kind of visual (such as Line, Transient, or Off), and the last screen which showed no visuals (such as Now-Next or Track). Tends to work best after you've explicitly selected those modes from the main menu as opposed to cycling through them with the info button.

But I will ask if there's a way to keep Line mode from squishing the visual.

Once upon a time, Line mode did not squish the visual, it covered the bottom of the visual instead of squishing it. A bunch of people complained and begged for the current behavior to be implemented instead. I've said it before: Be careful what you wish for, people.