So, DoC is not MtG, but there is an obvious correspondence between factions and colors:
haven = white
stronghold = green
necropolis = black
infernal = red
sanctuary = blue
The play styles and creature types tend to correspond properly, generally leading to overall balance (e.g. haven gets good defense, stronghold has huge creatures, infernal has high attack, etc.) in theory. In practice, not everything corresponds, and spell schools are a function of the hero and not the faction. So defensive white can cast black removal spells thanks to that knight hero. However, unlike MtG, you always have 4 colorless mana to cast either a 4 white creature or a 4 black spell. So abilities that are strong within a particular color, but are in a sense the defining characteristic of that color, become overpowered when given to a faction that isn't supposed to have them and already has their own trick. E.g. in MtG green gets regenerate, giant growth, and overrun, not black. If black wants that AND the ability to resurrect AND insta-kill AND fly AND deathouch etc, it risks not having enough mana to do it all. The mana you put towards overrunning your vampires gives you fewer vampires. But in DoC, you just pick whichever hero has whatever schools you want and proceed to puppet enemies as haven without tradeoff.
So one problem is the mix and matched color flavor between creatures and spells. Another is the mixup of red and green from MtG to DoC. Pick red/infernal and win fast, with creature nukes, hero nukes, and fast, damaging creatures. Well, no, because it's actually stronghold that avoids summoning sickness. Further, their heroes get access to lightning bolt and earthquake. This means a red deck can't ever actually do damage: play main attack creature (3+ might) with summoning sickness, get blocked by 7 health non-wall creature (wtf?). Play strongest creature, which if blocked still can't kill it (ravager), but die to green or air nuke anyway (earthquake/lightningbolt) (wtf?). Play fast red spells to nuke hero (altar) ... actually slow your own deck down by inhibiting draw. So you play it at the end of the game, but then it's just wasting hand space and sometimes you cannot fully utilize your resources because you aren't about to pay to *not* draw a card! Altar is a "must have" card that I never want to actually see in my hand. Red in DoC is a weird mix of not fast (summoning sickness), low on direct nukes (slow altars, mere 2 damage firebolts, of course there is massively OP fireball and firestorm but these can't damage heroes), and no creatures that survive the slightest counternuke ... spells which are supposed to be primarily for red in the first place yet are available to everyone! I expect to lose a ravager to RED or BLACK, not white/green/blue (blue can unsummon or counterspell, if they have mana, neither of which is an issue in DoC because you only play on your turn), and I expect to lose it after it attacks something. Well, maybe not quick attack ravager...too op...but why is quick attack not an infernal thing? Hounds are pretty awful but give them quick attack and suddenly an inner fire swipe actually does something. Give a hound king pack leader creature that buffs other hounds like the goblin king. Something. As it stands, infernal is the "nuke and win fast" faction that ironically gets nuked and loses fast. The fact that Lilim is seen as a good creature should indicate the problem, giving less attack than must have DAs (neutral and cheaper in resources than juggernaut...wtf) at twice the resources, and less attack then the main attackers (jug/ravager). It's purpose is entirely to sit there with 8 hp, and it's expensive for a "rush" faction. Of course, it will still be puppeted and insta killed half the time but the other half it will perhaps block something briefly, after which time you will lose because kelthor just sacrificed a 47 health 2 cost elephant to kill it while adding 40 rage damage for fun (and not consuming the rage (wtf?))
With limited experience with other factions I am not sure of the oddities that hurt others as much, though from playing against haven my primary thought is "I sure hope I draw fireball".
haven = white
stronghold = green
necropolis = black
infernal = red
sanctuary = blue
The play styles and creature types tend to correspond properly, generally leading to overall balance (e.g. haven gets good defense, stronghold has huge creatures, infernal has high attack, etc.) in theory. In practice, not everything corresponds, and spell schools are a function of the hero and not the faction. So defensive white can cast black removal spells thanks to that knight hero. However, unlike MtG, you always have 4 colorless mana to cast either a 4 white creature or a 4 black spell. So abilities that are strong within a particular color, but are in a sense the defining characteristic of that color, become overpowered when given to a faction that isn't supposed to have them and already has their own trick. E.g. in MtG green gets regenerate, giant growth, and overrun, not black. If black wants that AND the ability to resurrect AND insta-kill AND fly AND deathouch etc, it risks not having enough mana to do it all. The mana you put towards overrunning your vampires gives you fewer vampires. But in DoC, you just pick whichever hero has whatever schools you want and proceed to puppet enemies as haven without tradeoff.
So one problem is the mix and matched color flavor between creatures and spells. Another is the mixup of red and green from MtG to DoC. Pick red/infernal and win fast, with creature nukes, hero nukes, and fast, damaging creatures. Well, no, because it's actually stronghold that avoids summoning sickness. Further, their heroes get access to lightning bolt and earthquake. This means a red deck can't ever actually do damage: play main attack creature (3+ might) with summoning sickness, get blocked by 7 health non-wall creature (wtf?). Play strongest creature, which if blocked still can't kill it (ravager), but die to green or air nuke anyway (earthquake/lightningbolt) (wtf?). Play fast red spells to nuke hero (altar) ... actually slow your own deck down by inhibiting draw. So you play it at the end of the game, but then it's just wasting hand space and sometimes you cannot fully utilize your resources because you aren't about to pay to *not* draw a card! Altar is a "must have" card that I never want to actually see in my hand. Red in DoC is a weird mix of not fast (summoning sickness), low on direct nukes (slow altars, mere 2 damage firebolts, of course there is massively OP fireball and firestorm but these can't damage heroes), and no creatures that survive the slightest counternuke ... spells which are supposed to be primarily for red in the first place yet are available to everyone! I expect to lose a ravager to RED or BLACK, not white/green/blue (blue can unsummon or counterspell, if they have mana, neither of which is an issue in DoC because you only play on your turn), and I expect to lose it after it attacks something. Well, maybe not quick attack ravager...too op...but why is quick attack not an infernal thing? Hounds are pretty awful but give them quick attack and suddenly an inner fire swipe actually does something. Give a hound king pack leader creature that buffs other hounds like the goblin king. Something. As it stands, infernal is the "nuke and win fast" faction that ironically gets nuked and loses fast. The fact that Lilim is seen as a good creature should indicate the problem, giving less attack than must have DAs (neutral and cheaper in resources than juggernaut...wtf) at twice the resources, and less attack then the main attackers (jug/ravager). It's purpose is entirely to sit there with 8 hp, and it's expensive for a "rush" faction. Of course, it will still be puppeted and insta killed half the time but the other half it will perhaps block something briefly, after which time you will lose because kelthor just sacrificed a 47 health 2 cost elephant to kill it while adding 40 rage damage for fun (and not consuming the rage (wtf?))
With limited experience with other factions I am not sure of the oddities that hurt others as much, though from playing against haven my primary thought is "I sure hope I draw fireball".