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BNC's interesting discoveries in a convenient place. All credit to BigNailCow of the Shining Force Central Forums.
I've added some notes and clarifications in parenthesis. Someday, I might even get around to changing them to brackets so they aren't confused with the parenthesis in the original text.

Edit 11/25/2018 I added some parts of DarkKobold's TAS notes for future reference. Taken from http://tasvideos.org/2566S.html

1. Promoted Classes do 125% damage (also healing) with spells.

2. There are 6 unused bits in the spell resistance field for monsters/characters, and I found where it maps elements to spells. This means someone could add 3 more elements, theoretically, or expand the number of types of resistances, including maybe adding complete resistance and absorption. I also believe the "other resistance" option in SF2Edit could actually be resistance to status effects, but more testing is required.

3. Spell Crit Chances:
1 in 32 - Blaze, Freeze, Blast, Katon, Dao, Apollo, Shining Ball, Blizzard, Snow Breath 
1 in 16 - Neptun, Flame Breath, Kiwi Flame Breath 
1 in 8 - Bolt, Raijin, Atlas, Holy Thunder, Kraken Bubble Breath, Odd Eye Laser 
never - Demon Breath
(Additional note: Katon and Raijin are non-elemental and therefore unaffected by resistance/weakness)

4. The additional damage for a crit is determined before factoring in resistance. Since that's 25%, that means a crit is technically more effective when the enemy is majorly resistant. Since the damage goes from 100% to 50% when majorly resistant, then you add 25% of the original value, the crit is mathematically 50% of the damage it would normally be. So +50% for major resistance, +33% for minor resistance, +25% for no resistance, and +20% for weakness. 

5. When cursed, there is a 1 in 4 chance you will be stunned and have your turn wasted when attacking. Cursed does not manifest when using magic.

6. The programmers made a mistake. They didn't mean to call him "JAR". They entered the last byte of his name as a zero instead of an "O", so it was treated as a null byte.

7. I don't know if it's been done before, but I've finally confirmed exactly how the "special ability" value in characters' stats works (and by the way, I assume "???" in SF2Edit for class definitions is actually this special ability value.)

It's actually a bitfield, so if you don't understand binary you won't really know how to read the values. But long story short, it controls counter attack chance, double attack chance, and critical hit chance/severity. It's not really "special ability" at all so much as it is "dexterity" or something similar.

The lowest 4 bits (values < 16) control critical hit chance and severity, by referring to a table. Here are what the values mean:

0000 (0) = 1/32 chance of 150% damage
0001 (1) = 1/32 chance of 125% damage
0010 (2) = 1/16 chance of 150% damage
0011 (3) = 1/16 chance of 125% damage
0100 (4) = 1/8 chance of 150% damage
0101 (5) = 1/8 chance of 125% damage
0110 (6) = 1/4 chance of 150% damage
0111 (7) = 1/4 chance of 125% damage
1000 (8) = no chance of critical

The other 7 values all seem to be a 1/4 chance of 150% damage, but it doesn't display "heavy attack". This seems to be a "secret crit" option.

The next 2 bits (16 and 32) control double attack chance. It goes from 1/32 to 1/4 as you increase the value.

The final 2 bits work for counter attack chance in the same way.

The best possible value you could have is 246 (11 11 0110).
That's 1/4 counter, 1/4 double, 1/4 150% crit.
Quite impressive.

So let's look at some examples:

Most normal unpromoted classes:
3 = 00 00 0011 = 1/32 counter, 1/32 dbl, 1/16 125% crit
Most normal promoted classes:
67 = 01 00 0011 = 1/16 counter, 1/32 dbl, 1/16 125% crit
Baron class:
68 = 01 00 0100 = 1/16 counter, 1/32 dbl, 1/8 150% crit
Master Monk and Wolf Baron classes:
131 = 10 00 0011 = 1/8 counter, 1/32 dbl, 1/16 125% crit
Red Baron class:
132 = 10 00 0100 = 1/8 counter, 1/32 dbl, 1/8 150% crit
Ninja class:
148 = 10 01 0100 = 1/8 counter, 1/16 dbl, 1/8 150% crit

In conclusion:
- Baron has new usefulness as it gets better crits.
- Ever wonder why Lemon gets his own class? Because they wanted him to be better at countering than Barons.
- Slade is seriously badass.

Now some monsters:

- Several monsters seem to secret crit...
- Ever think Kraken Legs are a bit unfair? You're right. They have 1/16 counter, 1/16 dbl, and 1/4 150% crit. Several other monsters have this, but doesn't it always seem like Kraken Legs are particularly destructive?
- Particularly impressive bosses:
Zalbard, Galam = 1/4 counter, 1/8 dbl, 1/4 125% crit
Cameela, Red Baron, Zeon = 1/4 counter, 1/4 dbl, 1/4 125% crit
Odd Eye = 1/4 counter, 1/8 dbl, 1/4 150% secret crit

8. Apparently the game caps base MOV at 9. Did we know this before? You can still get to 11 by equipping the Running Ring, but attempting to use a Running Pimento when your MOV is 9 will get you +0.

9. Wasn't the conventional wisdom that Kiwi's flame breath doesn't upgrade? Well, it does. At level 12, 20, and 30. I also found that the probability of him using it is 1/4, or 25%.

Actually, I think I screwed up and it's level 32, 40, and 50, promoted.

10. High accuracy characters are considered to be BRGN, ACHR, SNIP, and RNGR (Maybe they're not so useless!) 
(clarification: This is based on movetypes, not classes. Basically, if someone uses arrows this applies to them.)

Normal dodge rate is 1/32. 
If a normal character attacks a flying or floating character, the dodge rate is 1/8. 
If a high accuracy character attacks a flying or floating character, the dodge rate is 1/32 again (this means they are 4 times as likely to hit flying or floating characters, or the dodge bonus is negated). 
If the attacker is muddled, the dodge rate is 1/2 (ouch!)
(Also: Attack is increased by 25% For Bow Users vs. Fliers and Floaters)

11. It would seem the Counter Sword, Iron Ball, and Taros Sword only have a 1/32 chance of dropping. All the other items that drop are 100%. 

12. The deals section can store up to 15 of the same item.

13. You cannot counter-attack Taros. Even Bowie.

14. (Credit to Loftus for this one) Ranged counters give no xp.

15. A debug code I just found (apologies if everyone knew): 
As somebody's turn ends in battle, be holding A+B+C+Up on player 1. All enemies will instantly die and you win the battle!

16. I am now almost positive that chirrup sandals have no effect on the enemy AI.

17. Mithril Weapon Creation
There are 4 weapons for each type, and it goes: 
The rarest weapon has a 1/16 chance. 
The 2nd rarest has a 1/8 chance. 
The 3rd rarest has a 1/4 chance. 
If none of those, you'll get the most common. 

These are all separate checks, meaning it generates a random number, and if it's not the 1/16, it moves on to the next weapon and generates another random number. 

18. Randomized AGI for the purpose of turn order is anywhere from 7/8 to 9/8 of the original value, then augmented by -1, 0, or 1 randomly. If it's over 128, the second turn is 7/8 to 9/8 of 5/6 of the amount of original AGI over 128.

19. Land Effect Equation: damage * x / 256 

0xabe2 - 0% land effect value (0x0100, 256) 
0xabec - 15% land effect value (0x00e6, 230) 
0xabf8 - 30% land effect value (0x00cd, 211)

(To cut out the need for math
0% = Full Damage. Duh.
15% = ~90% Damage. So about 10% reduction. Damage * 0.8984375
30% = ~82% Damage. So about 18% reduction. Damage * 0.82421875)

20. Non-Magic Attack damage calculation.
The full process for determining damage is:
- Attacker ATT - defender DEF.
- Apply land effect.
- Subtract a random amount between 0% and 25%, unless it's a Burst Rock (?!). I think this is weighted to fall normally around 12%, but I'm not good with statistics.

DarkKobold:
	RNG Manipulation
		The RNG of SF2 is a 16-bit sequential loop. It can only change for one of three conditions: A call for a random value, a text 
		box pause, or sitting in a menu. For the two ones that can be manipulated, the RNG advances one step per frame. To cycle 
		through all 65,536 values of the RNG would take 18 minutes! Additionally, this also means I only get 1 chance to access the RNG 
		per-character turn, which limits my ability to manipulate the enemy movements, attacks, and etc. While most worthwhile 
		attacks/rounds are available within the first 60 frames, there are a few waits that are a few hundred frames long, 
		unfortunately. I did my best to minimize wait time in menus.

	Attack Power and Leveling
		The single most important factor to making this run is attack power. For the majority of characters, 1 attack is the most they 
		can gain per level. The three characters used in the run all have the ability to gain more attack, +2 for Bowie and Slade, and 
		+3 for Peter. However, these values are rare for the early, unpromoted levels (~10-20% for Peter and Bowie). Unfortunately, 
		this system also means that quite a few enemies must be killed that otherwise wouldn’t be obstacles to the boss sniping. Also, 
		as a side note, this system is ridiculous for a TAS. If you figure that +2 for Bowie and Slade is essentially gaining 100% more 
		attack, then every +2 you get is like gaining two levels. Luckily, the game does not change the probability based on your 
		current attack. This makes for an absurd amount of attack for Peter at the end of the game.