Thought I'll document these AI behaviours here. Note that these AI behaviours are from the recent Galakrond patch, which might change when future PvE contents are made.

---2021 update: These behaviours doesn't apply anymore. Corrupting Mist + Taunt isn't a reliable combo anymore---

Doomsayer vs Depth Charge AI's reaction:

AI knows how to play around Doomsayer. They'll kill the Doomsayer if they have >=7 damage on board. And if they don't, they'll have their minions attack your face. They won't be putting any new minions on the board, knowing that it'll get killed by the Doomsayer.

They don't do this against Depth Charge though. If they have <5 damage on board, they'll still play new minions even if it have <=5 health, not knowing the Depth Charge will kill it immediately. The existing minions will also attempt to damage Depth Charge, probably because they still consider Depth Charge a high-priority target to damage (which saves your hero's health).

I've seen few bosses who acts differently with Doomsayer though, where they might still play minions even with a Doomsayer on board.

• Sun Raider Phaerix: Don't know why, but if you have Doomsayer on early game (such as turn 2), he'll still play his minions into the Doomsayer. At first I thought he wants to trigger the deathrattle of his 5/5 Tolvir Hoplite (deal 5 damage to both heroes), but I've seen him wasting his Wild Pyromancers too.
• Rafaam and Galakrond: The AI in Rafaam phase is probably coded to play Invoke cards whenever possible, so he'll still play his Invoke minions and summon his Imps even with Doomsayer alive.
• Avalanchan: Happened on my recent attempts, where the AI wasted his Water Elemental and Frost Elementals with Doomsayer on board. Maybe they made the AI prioritise in playing these minions, for story flavours?

Corrupting Mist your Taunt, and AI's minions won't hit your face:

Here's how AI usually behave when their minions got hit by Corrupting Mist:

1. They're likely to trade against your non-corrupted minions, probably thinking that's the most valuable move since their minions will be gone next turn.
2. They will not trade on your corrupted minions, knowing it'll die next turn anyway

Behaviour number 2 also applies if your taunt gets corrupted, they won't bother trade against your taunt. This ensures your face won't be hit, even if it's just a small taunt against lots of AI minions.

AI might still use spells to damage the corrupted taunts, but they will still not trade if the taunt doesn't die from the spell.

This behaviour also applies on your Doomsayer or Depth Charge. You can use Corrupting Mist on them and AI will ignore it, allowing their effect to trigger next turn.

Demo video of this behaviour: www.youtube.com/watch?v=iXWOmxjUKMo