but does that allow it to be skipped? Nothing else in the game should be happening except waiting for this entire trigger to run.

erm... what?
wait block means you run 2 waits (transmission, and in single player move screen is a wait too) in 2 different triggers the same time for the same player.
Just replace one wait with death counters. Maybe it's even your hyper triggers blocking. Give them to a player without waits.

Eh... I can't explain well >_< Okay, given that it does have a wait block. I inserted a line after one of the waits to modify resource to 50k. The line still fired despite the previous centerview and display text lines.
Like so:

wait 5000
Centerview at 'pl1'
Display text for current player
Modify resource for current player to 50,000 ore.

The last line seems to fire on time while two lines previous to it do not fire at all.

If the resources are given the other actions are processed too. That's a fact. It's impossible that certain actions are skipped (except you used actions like creating units for P12 or display text/center view for a comp player, which is illegal and therefore ignored).
I assume then that the trigger is not running for the right person, because your 'current player actions' (like center view, display text) are not firing.

Other possibilites:
'pl1' is not where you expect it, so the center view does take place but somewhere else (e.g. where your screen currently is)
Display text has an empty string or too many blank lines at the end or is overwritten by another trigger executing other display actions.

Although I understand that there are no way triggers are simply "skipped", I do know that sometimes when text is displayed and a moving unit is occupying the text display area, the text is "erased" as in it disappears where the unit moves.

even if pl1 is in the wrong location, there should at least be a noticeable centerviewing to somewhere.

I was wondering if the Players were wrong, but I also set the mineral modification to "current player" and it fired off just fine... would default "current player" trigs be the problem? Since "Centerview" and "Display Text" both are defaultly for "Current Player", while modifying minerals is a selected player (to current player).
If I do centerviewing on Force 1, force 1 consisting of players 1-4, that should make all 4 players centerview to a common point as well as receive the same displayed text if given, right?

Sorry, I'd post the map, but I'd already fixed it so it'll have to happen again for me to show you.

No, "Current Player Trigs" cannot be a problem.
And center view cannot be done for force 1, It's fixed to run for current player. If you have it owned by a force the triggers are split up and every player runs an individual copy.
That means if the trigger looks like this:

Force1:
If Switch 1 is cleared
Display Text
Set Switch 1
preserve

Then your trigger will fail! Because the first player runs it, gets the message and sets the switch. When the 2nd player (remember it's being split up!) checks the trigger the switch is set and thus will not run.
You would have to set a death counter for force 1 (sets it for all players in the force) and make another trigger which, dependent on the dc, runs the display text and resets the dc for current player.