Ex. What would be right:
- ... that caught everyone's eye.
- ... that caught everyone's eyes.
Ex. What would be right:
The idiom is "to catch someone's eye," meaning to draw someone's attention, and when it's just one person, there's no problem. I say, "She caught my eye." I would never say "She caught my eyes." But what happens when she catches the attention of everyone in the room? Did she catch everyone's eye? (One eye per person, as the idiom directs) or did she catch everyone's eyes? (one eye per person times many people is many eyes)
The google finds that the plural "eyes" far outnumbers the singular "eye," but the reverse is true for the books they've scanned.
In the example from an opinion written by Judge Richard Posner (link in DRF's comment), the judge writes of ostriches with their head in the sand, probably because "ostriches with their heads in the sand" conjures up the uncomfortable image of multi-headed ostriches. This problem doesn't arise with eyes, so the choice is up to you.