Gambler's Strike seems to work as advertised when you auto-resolve the battles - I've killed my own champs with it that way. However, in tactical combat it doesn't seem to do double damage nor does it have a chance to strike back at the hero - it seems instead to just be a guaranteed hit normal attack.
Another few that are off:
Sweep. This ability is supposed to do 50% of normal dmg to all surrounding targets. My hunch from seeing it in action many many times is that it does 150% normal dmg. It also bugs out with some characters where the animation doesn't quite complete - no sound played after it hits for damage, and no damage is done. This also causes the game to 'hang' for about 5-10 seconds. The sweep not doing dmg bug is specific to characters - or perhaps equipment. I'll see the bug every time I attempt to use it in certain games with certain characters, but never with others.
(Seems to me, if I recall correctly, the last two times it bugged out for a character was for *mounted* characters using staff weapons, but I haven't confirmed that the staff or mount or combination was the issue - or whether it was the particular character (both times were custom female sovereigns with Porcipines headband and the magic staff that sovereigns can choose as initial options).
Channeled casts. Occasionally just fail to go off. They don't even get listed in queue, it's not that they get interrupted, but the mana is still consumed on cast. I've seen this with blizzard, fireball, and titan's breath,
Move & Attack: Occasionally units will move and automatically attack even though you've clicked the square you are going to, not the square you're attacking. This prevents the use of special abilities that would be needed.
Equipped weapons with maul: These will fail 100% of the time on the second attack, even with lvl 45 champions with 100 accuracy. If you hover the mouse pointer over the unit you're attacking, you'll see the odds for the attack go from 100% on the first swing to 0% on the second very briefly.
Spell cost reductions (from Affinity, Path of the Mage, Mantle of Oceans or equipped gear) do not work on autoresolved battles. They do work in the tactical map, but even here there are bugs.
Here is one example of a spell cost reduction bug. Obtain a hero with a base 50% magic reduction (mantle of oceans, or path of the mage + affinity). Equip this hero with Archmage robes (40% reduction). Most spells here will now list at a zero cost on the tooltip, and can in fact be cast when you are at zero magic. However, they are still using some fractional amount of mana which the game seems to track behind the scenes. One cast will cost nothing, then the next cast will cost 1 - even though the tooltip shows the cost as 0 - zero. This can cause your mana to drop to negative values - e.g. -1, -2, etc.
Once you are into negative mana from this bug, any of your imbued heroes or sovereign can now cast any spell no matter the cost, which will then push your mana further into the negative. If you maintain your mana below zero, you have limitless spell casting in every tactical battle.