Thieves' Auction is cast with Grip of Chaos, Confusion in the Ranks and some other permanents on the battlefield -- how will the mess be resolved? Does everything enter at once, or is the order in which the cards are 'drafted' matter?

Specific example

Grip of Chaos is irrelevant to the Auction, so I can only assume you're asking how it interacts with Confusion in the Ranks. The answer to which is that, when the Grip ability associated with each Confusion trigger resolves, the target will be chosen at random from among all viable choices.

In the specific example given, Player 1 will choose targets for Confusion in the Ranks first, followed by Player 2 (who also chooses where Palinchron's trigger is stacked in rgeards to his/her Confusion triggers), then 3, then 4. Then Grip will trigger and Player 1 will choose the order in which his Confusion triggers have their targets rechosen, followed by Player 2, then 3, then 4. Player 4's Grip triggers will resolve first, followed by Player 3's, then 2's, then 1's (assuming everybody passes priority). This is when the chaos really starts: Player 4's top-most Confusion in the Ranks trigger will resolve, targeting whatever was chosen at random by the Grip. With exception to lands, everything you listed will have triggered Confusion in the Ranks. So, Player 4 has two creatures and an artifact to exchange. Those actions will be done. If any of those swaps were targeted by another Confusion trigger controlled by a player other than whoever gains control of it, when that trigger resolves another swap will be made (so if from Player 4's triggers Player 3 gains control of a creature he or she had to target, the swap will not be made when Player 3's trigger resolves).

Now, Palinchron introduces an interesting twist to the scenario. Because its trigger doesn't target. So Player 2 could potentially have enough mana to bounce it if, AND ONLY IF, Palinchron does not get swapped out to any other player (or somehow makes it back to Player 2) before his/her Confusion triggers start resolving. Or s/he could untap enough lands of whoever ends up controlling Palinchron so they can bounce it. But in the scenario described, I don't think that would consistently happen.

In regards to Angelic Destiny, I believe that Player 2 will have a choice of Palinchron and Serra Angel to put it onto. I'm double checking the Comp Rules right now to see. Although I predict that if I am wrong (80% sure, in this case), then all creatures on the battlefield will be viable choices to attach the Destiny to (also 80% sure I am wrong about this).

Edit: If I'm reading this correctly, my initial assumption is correct about Destiny.

Thank you! That gives me a great deal of insight into how to untangle this mess should I ever successfully create it.

Post-it notes for the stack are going to be vital.