Does a monster need to inflict 1+ combat damage in order for this Exhibit to work?

I don't see why not. It does specify "and any abilities that add a special effect to combat damage," which would largely be irrelevant otherwise.

Walk said:

Yes, the monster has to deal its combat damage. However, this doesn't necessarily mean your Investigator has to TAKE that damage. I suspect the only reason you're asking this question is because both of those conditions came up. Say, if Michael missed a one-combat-damage monster, someone had Enchanted Jewelry or Food, or Leo was in play?

Basically, if you missed your Combat Check (or an Evade Check), the monster officially "deals its damage"--plus any extra conditions, although the only monsters with extra conditions that don't leave you devoured are Elder Things (lose an item), Children of the Goat (delayed), or the Shugeron Mask (doom token), and you'd have to have lowered the toughness of two of them with a Red Sign and/or a Sledgehammer--but there are a few ways that damage won't actually reach you. Once all that is done, you can activate the Exhibit.

jgt7771: I believe Esto was wondering about monsters such as Child of the Goat or the Nightgaunt, which never deal damage.

Esto: Sorry, I subtly but direly misworded it. What I meant to indicate is that Image of the Dark Pharaoh can always be used, even if the monster doesn't deal damage. My reasoning was that the card specifically mentions special effects that accompany or replace damage.