I think Alucard mentioned most of the most important ones. Khelly bug, ingot bug, and "Skilled" are the most important because they crash the game. Piety overflow I would also rate as quite important, because it is an easy and cheap exploit. But let me mention some more that haven't been mentioned:

- Darkness does not work as normal on door squares. A monster standing on a dark door square always sees the player.
- It is possible to rob some shops without getting noticed by the shopkeeper by digging the walls, putting items in a corner of the store, and then kicking them diagonally. The shopkeeper can blatantly see you doing this and won't notice. You can see more info about this bug on: http://ancardia.wikia.com/wiki/Kick-robbing
- Background corruption only increases once, on day 90. Correct me if I'm wrong but I have seen here that it was supposed to increase again on day 180, etc. If it is so, this would be an important bug since the game is not as difficult as planned
- Fireproof blankets work better if you are doomed in the Tower than if you are not doomed.
- I don't know if this is a bug or an intended feature, but in the Casino, you can play as long as you wish with a slot machine without getting any corruption. Perhaps it was intended, but I feel there should be a downside to putting a paperweight on top of the space key and getting millions on the slot machines.
- I'm sure some more experienced (or scummy) player will be able to complete this, but I think there is a really abusive exploit with the monk's circular kick. Something like that when there is a pet adjacent to you, the circular kick takes no turns at all and you can repeat it indefinitely without the monsters being able to do anything. I don't remember the details of this one, can anyone elaborate?

I don't have an iPad so sadly I won't build that version (I'd be willing to pay for ADOM, but not for the iPad...); but I hope everything goes well, and we can enjoy the bugfixes in regular ADOM!