Most of these have been known for years, others I have never cared to share.
Obviously, I did not find all of these peculiarities myself.
Some of these were found by Acro or KartSeven and a whole lot of other people. In fact, if you happen to be fluent in French, you can read about hundreds(!) more of these at ff7.fr .
Also, you are not really supposed to know any of these unless you are at the height of a powerful obsession with Final Fantasy VII. Actually, I'd be interested in learning how many of these were known to you, so tell me if you don't mind.
01 - 00:00:05 - Lose Final Fort Condor Battle
02 - 00:01:03 - Unsellable weapons
03 - 00:01:12 - 100 Atk: Ultima Weapon, Flayer
04 - 00:01:19 - Conformer attacks allies
05 - 00:01:43 - Ribbon is not deathproof
06 - 00:01:51 - Poison Ring: 10,000 Gil
07 - 00:01:56 - 1.4 million Gil materia
08 - 00:02:03 - Quadra Magic: KotR, Escape
09 - 00:02:17 - Quadra Magic: MP cost
10 - 00:02:39 - Magic Pot steals
11 - 00:03:06 - JORG Super Nova
12 - 00:03:33 - Final battle: Sephiroth's attack
13 - 00:03:50 - Final battle: No Counter Attack materia
14 - 00:04:02 - Final battle: Sephiroth takes no damage
15 - 00:04:26 - Final battle: Lucky 7s
16 - 00:05:21 - JORG Whirlwind Maze FMV
17 - 00:05:56 - Gaea's Cliff: Body temperature
18 - 00:06:04 - Gaea's Cliff: Body temperature decline
19 - 00:07:02 - 16 Elements
20 - 00:07:17 - Ultima is missable
21 - 00:07:41 - Pandora's Box: Global variable
22 - 00:08:31 - Emerald's AI: Bahamut summons
23 - 00:09:57 - Underwater materia AP
24 - 00:10:04 - Darkness status
25 - 00:10:35 - Game Over at the beginning of a battle
26 - 00:10:50 - Skip Shiva
27 - 00:11:24 - Pre-emptive boss battles
28 - 00:12:03 - Healing Overflow
29 - 00:12:08 - Damage Overflow - HP Absorb
30 - 00:12:19 - Vincent's Mug Glitch
31 - 00:12:29 - Midgar Skip
32 - 00:12:47 - Midgar Turks Skip
33 - 00:13:06 - 198 copies of an item
34 - 00:13:27 - Ultimate Weapon respawns
35 - 00:13:46 - Ultimate Weapon's HP
36 - 00:14:02 - Inescapable Battles Glitch
37 - 00:14:33 - Ruby Weapon uses Whirlsand
38 - 00:14:57 - Ruby Weapon Battle Glitch
39 - 00:16:08 - Emerald Weapon's Eyes
40 - 00:16:29 - Trickplay: Gold Mountain
41 - 00:16:53 - Super Nova, KotR animation lengths
42 - 00:21:08 - Mystery Ninja encounters
43 - 00:21:35 - How to lose the Highwind
44 - 00:22:33 - Sephiroth is not invincible
45a-00:22:54 - Expulsion attack flags
45b-00:24:07 - Pseudo-pre-emptive battles
46 - 00:24:35 - Back attack damage
47 - 00:24:56 - Aerith's equipment after Demons Gate
48 - 00:25:48 - Limit Bar mechanics
49 - 00:25:59 - Fat-Chocobo chance
50 - 00:26:23 - Gunge Lance
51 - 00:27:03 - 255 Attack% Weapons
52 - 00:27:14 - Masamune deals critical hits
53 - 00:27:18 - Leaving Wutai during the sidequest
54 - 00:27:47 - Freezing the game with Reflect
55 - 00:28:45 - Teioh loses
56 - 00:29:11 - Slow-numb status
57 - 00:29:49 - Emerald Weapon uses Aire Tam Storm
58 - 00:30:12 - Aire Tam Storm drains damage
59 - 00:30:25 - Ignore Defense/Magic def
60 - 00:30:36 - Hidden weapon boosts
61 - 00:30:51 - Chocobracelet
62 - 00:30:59 - Ziedrich
63 - 00:31:09 - Blade Beam
64 - 00:31:46 - Dragon Scales, 8-inch Cannon
65 - 00:31:58 - Limit Breaks miss
66 - 00:32:17 - Sneak Attack Glitch
67 - 00:32:52 - Death Weaknesses
68 - 00:33:43 - Status effects as elements
69 - 00:34:35 - Auto-critical Limit Breaks
70 - 00:35:37 - EXP at Level 99
71 - 00:35:53 - Natural HP and MP
72 - 00:35:58 - Damage Overflow by other characters
73 - 00:37:54 - Yuffie steals materia
74 - 00:38:59 - Huge Materia in Bugenhagen's observatory
75 - 00:39:22 - Cover Overflow
76 - 00:40:00 - White Wind removes Death Force
77 - 00:41:13 - No Game Overs
78 - 00:41:47 - Aerith's death FMV
79 - 00:42:37 - Bone Village Inn
80 - 00:43:07 - Maximum BP at Battle Square
81 - 00:43:13 - Gondola rides with other characters
82 - 00:46:07 - 3D Combat minigame
83 - 00:46:40 - Character reactions to Aerith's death
84 - 00:47:44 - Cait Sith's Bar Summons
85 - 00:48:24 - Cait Sith's Game Over, Death Joker Slots
86 - 00:48:52 - Highest enemy stats
87 - 00:54:11 - Gongaga is not on the world map
88 - 00:54:21 - Carob Nut
89 - 00:54:56 - Gold Chocobo breeding RNG exploit
90 - 00:55:02 - Impaled Midgar Zolom scene
91 - 00:55:23 - Materia inventory
92 - 00:55:39 - Miss Kujata
93 - 00:55:54 - Godo heals Yuffie
94 - 00:56:09 - Sense mechanics
95 - 00:56:25 - Level 1 Cid
96 - 00:56:32 - Multi-elemental attacks
97 - 00:58:55 - Strange walkways
98 - 01:01:49 - Revive enemies
99 - 01:04:43 - Elixir Cover Glitch
100-01:05:10 - Unusual enemies