Things I thought of that probably aren't relevant; feel free to just skip answering if none are relevant - I'm having a hard time parsing out which things are relevant here:
Healing Wish / Lunar Dance - I assume they don't care about turn history. It looks like they stack FIFO? Would that change if one were before 255 and one was after (i.e. the game would look at the move order to see which one was used first to see which should come off the stack first, or is that info stored elsewhere?)
2-turn charge moves - again, probably not in the same category, but what would happen if you used Meteor Beam across the 255?
On the other hand, if you Hyper Beam on 255, will turn 1 remember that you need to recharge?
Wrap might be interesting. Could you infinitely trap someone?
Sleep; either Rested or random
I'm assuming defense curl is a status, and rollout/ice ball don't just check to see if the move was previously used?
Same assumption for stockpile, charge?
Lock On
Protect / Destiny Bond / Endure success
If you switch in on turn 254, waste turn 255, and then when it rolls over, does Mat Block work (again, if this works in Gen 7)
Mimic / Sketch / Instruct
Does Last Resort know you've used all other moves if you rolled over?
Is Yawn a status?
Gigaton Hammer?
Healing Wish / Lunar Dance - I assume they don't care about turn history. It looks like they stack FIFO? Would that change if one were before 255 and one was after (i.e. the game would look at the move order to see which one was used first to see which should come off the stack first, or is that info stored elsewhere?)
2-turn charge moves - again, probably not in the same category, but what would happen if you used Meteor Beam across the 255?
On the other hand, if you Hyper Beam on 255, will turn 1 remember that you need to recharge?
Wrap might be interesting. Could you infinitely trap someone?
Sleep; either Rested or random
I'm assuming defense curl is a status, and rollout/ice ball don't just check to see if the move was previously used?
Same assumption for stockpile, charge?
Lock On
Protect / Destiny Bond / Endure success
If you switch in on turn 254, waste turn 255, and then when it rolls over, does Mat Block work (again, if this works in Gen 7)
Mimic / Sketch / Instruct
Does Last Resort know you've used all other moves if you rolled over?
Is Yawn a status?
Gigaton Hammer?