I can't find any, but I figure I'd ask just to make sure ... is there any situation in 5e in which whether a spell or other magical effect is arcane or divine matter?  This is specifically arcane vs divine; I know, f'rex, that you can only use a scroll if it's on your spell list, but a Bard can, AFAIK, use any Cure Wounds scroll no matter who wrote it.

Not in 5e. I did a bit of searching on this, as I attempted to make a homebrewed subclass designed ot counter divine magic. Nowhere is a real distinction made, unlike in earlier editions.

In 5e the only thing that matters is that the spell is on your class spell list.

Spell list wise none.   A slight difference on what focuses you can use (orb vs holy symbol).  

Items might have class restrictions, but most act like scrolls (Is it on the spell list)

So its a vestige really, or flavor.

I forgot about different spellcasting foci. A sorcerer, warlock, and Wizard can all use the same arcane focus for their spells. A cleric and paladin can use the same holy symbol for their spells. Bards and druids use unique foci.

I would say it's intentionally left open to the DM so they can make that distinction as significant or not as they choose.  I would make the argument that if the source is from a Cleric, or from a Divine Soul Sorcerer, there's a pretty good expectation that the energies involved are of a Divine origin.