Are there any ingredients I should not add to a no-knead dough with an extended proofing time?
I don't think there's anything specific to worry about with bread dough.  The important point is the temperature: if you're considering adding an ingredient that you normally wouldn't let sit out at room temperature for 18 hours for food safety reasons (and/or because it might start tasting "off"), you probably should add that ingredient toward the end by folding it in before shaping or something.  

Most no-knead bread recipes that sit out at room temperature for a long time are quite flexible.  You likely won't cause any problems by folding in an ingredient late in the first rise.