These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Fight Scene Failure: The combat animations frequently involve no contact between opposing forces at all. War Bears, for example, damage their foes by nodding at them.
Game Breaker: The infamous Wraith: or Shadow Demon rush, as well as some of the high end spells, especially Armageddon, that provides a nigh-infinite supply of mana. Or paladin rush. Or a fleet of catapult-armed ships under Flight, Eldritch Weapon (optionally) and Spell Lock (dispel is hindered even more with Archmage, Runemaster and/or Sorcery Mastery). Or the self-maintaining time stop. That is, once you get resources to pull such tricks...
In the original version, a stack of two or three paladins could easily defeat pretty much anything the enemy would throw at you. They were later nerfed.
A certain combination of traitsnote Runemaster and Artificer allows a person to craft items at quarter price and then sell them for half price. That is, you spend 50 mana making a weak sword with listed price of 200, then break it for 100 mana. While it takes time to create a weapon like this and picking those traits cripples your spellcasting ability, it becomes very, very easy to very quickly start making items that cost thousands of mana (which you can do much faster than actually making thousands of mana), which means what little magic you can cast you can cast lots of — and any heroes you get are going to be wearing some very, very nice equipment.
Best way to run this is to have five blue picks, which lets all your heroes have no-maintenance un-dispellable Flight, as well as "bastard invisibility" (the AI can still see you, but can't target you with ranged attacks although spells and spell-like powers still work) and Magic Immunity. If you manage to get another couple of blue books during play then things get even sillier. Also, once you have a mana reserve you can put all your mana production into casting skill and research, especially the former.
Black Channels. Elite War Trolls. Your trolls are stronger, cost basically no upkeep, and unlike most Black Channeled units, still heal because trolls regenerate. They don't gain any experience, but that's why you do this on those you've already gotten up to Elite or Ultra-Elite...
Life magic has a spell that doubles the income of a city and another spell that makes citizens euphoric, thereby canceling all rebellion within a city. Combining these two spells on all your cities and jacking up taxes to three gold per turn will essentially give you an unlimited amount of gold, to the point where you can build a city or massive army from the ground up in just a few turns. Then again, gold is rarely in short supply late gamenote Late game? You can begin the game with Stream of Life, and get it cast on your first city. Taxes through the roof, and you can burn gold for mana to maintain your enchantment, with interest, and your population is booming. Rinse and repeat as you build or capture cities. It's a completely degenerate strategy, worth playing once just for the lulz, and food is more of a limiting factor on armiesnote Big cities can make you lots of food anyway than money, which is where Nature magic comes in ...
Many Game Breaker strategies are based on investing all starting picks in one spell school, which allows picking some high-level spells from the start. While it takes a lot of timenote though, in perspective, it's a lot less time than it would take to get a supply of Pikemen or Longbowmen on-line, let alone Paladins to actually cast this high level spell, once it's done you get unstoppable warrior (or some other overpowered thing).
Alchemy allows you to convert gold to mana; in the original game, it was at a one-to-one ratio, though it was nerfed in a patch. Generally, it is much, much easier to get gold than mana, especially in the late game; and there are many Life and Nature spells that raise gold income in a city — creating a feedback loop where you spend small amounts of mana to get huge boosts to your gold income, then turn the gold into mana and repeat the cycle... Even post-nerf, Alchemy is overwhelmingly powerful.
Flying Invisible Warships are also an infamous game-breaker. Unlike every other ranged unit in the game, warships have infinite ammo. Flight allows them to move on land and means non-flying units can't attack them. Invisibility means that as long as they keep their distance, only units who can see through illusions will attack them; and AI enemies don't automatically approach invisible units. There are almost no flying units that can see through illusions, so a flying invisible warship can simply pelt the enemy with ranged attacks until they die, with most units having absolutely no way to fight back. Even against the few units that can fight back, a warship is an extremely powerful unit, usually limited only by its inability to leave the sea... which flight negates.
Good Bad Bug: Occasionally Galley units would gain numerous properties and powers, becoming more powerful than any hero.