Early in King of Attolia, Eugenides gets fed up with his attendants deliberately misdirecting him and strides out ahead, confidently making his way through the palace only to hit a dead end balcony, leaving them laughing. It works into his Obfuscating Stupidity, but after he's revealed his true self later, he once more leads himself to the same dead end. Rather than go around again, he climbs down the balcony and up the other side—meaning that he's so used to it not being a dead-end for him he may not have even thought about it until he got there and realized he'd need to drop his facade to use that route.
Why would Immakuk and Ennikar, the mythic heroes of Medea, help out two people who are working against Mede interests? For one thing, they might be playing a long game (in that Medea being unable to invade might be better for them down the road). For another, their real-world inspirations of Gilgamesh and Enkidu spent quite a bit of their time making their own gods very angry.
Towards the end of Thick as Thieves, Costis falls down a dry well, and instantly all the men present assume he has been killed. Kamet runs away, and only returns because it occurs to them that Costis may be injured and dying slowly, rather than dying immediately—and then discovers that Costis doesn't have a scratch on him. It's a lucky coincidence, until one recalls that, at the end of King of Attolia, he had sworn an oath both to Eugenides (the king) and his god (the other Eugenides). The king promised him that he would never die of a fall unless the god himself dropped him.