Generally speaking, the missions that are retroactive are the ones referring to permanent progress - for instance, unlocking a certain bonus in the Great Hall. In theory, when a player gets to the 'unlock a level 4 Great Hall bonus' mission, they might already have level 4 on everything in the GH, so then they might be stuck forever if the mission required a *new* unlock. So it doesn't. Also for the missions referring to fusions (Justiciar, Relickeeper, Rhazin), it would be perhaps not impossible but extremely annoying and difficult to have to fuse the champion again, so the mission is retroactive and will auto-complete if you've done it in the past (in the beginning, the fusion missions were not retroactive but they changed that). 

This mostly also goes for the missions requiring a level 60 champ, requiring a champ to be equipped with gear and so on - though there is one notable exception, the series of missions requiring you to reach level 6 ascension on a champion of each affinity. Those are NOT retroactive, which has caused a fair bit of annoyance to people who expected them to be and suddenly had to ascend champions who they didn't even want to take to 6*. 

But missions requiring you to farm arena medals, or to reach a certain tier in arena, yeah, those are not retroactive, you're supposed to do that at the time when you are given the mission. Same goes for missions requiring you to run a certain dungeon stage, hit for X damage on the Clan Boss, and so on. 

ok, thanks, it is what it is

From what I remember, it is actually impossible to fuse champions like Rhazin a second time. Not sure about the others, though.

True, Rhazin can only be fused once - but Justiciar/Relickeeper can be done as often as you like, as can Broadmaw. Some people regularly fuse Broadmaw for extra points during champion chase tournaments. 

and the combine a sh!tload of potions was annoying.  though that will be much easier now with the 20 keeps.  Everything about the game is just so much easier now...