Some sidequests have "Limit 1 Copy in the Victory Display" but what happens if each player plays one? Can you still complete both sidequests but then the second just goes to its owner's discard pile?

I didn't search out the ruling, but I believe Caleb did issue one saying basically what you posit.

Correction: it's actually in the rulesheet for Sands of Harad (the first product that actually had such a side quest)…

The player side quest, The Storm Comes, has the text: "Limit 1 copy of The Storm Comes in the victory display." This text prevents more than 1 copy of The Storm Comes from entering the victory display. If the players defeat The Storm Comes, and there is already a copy of that side quest in the victory display, then the copy that was just defeated is placed in its owner's discard pile.