"He doesn't look strong," I said, studying the boy's skinny arms. (Prologue.32)
Many of the peculiar children look perfectly normal, like this kid. Some, however, don't, like Millard the invisible boy and the girl with a mouth in the back of her head.
The image was so strange, and yet it was nothing like my grandfather's pictures. There were no tricks here. It was just a woman—a woman smoking a pipe. (2.107)
The realistic-looking image convinces Jacob that this might be true. If it had been a goofy-looking one, Jacob probably would have written Miss Peregrine off as fantasy right then and there.
My grandfather had described it a hundred times, but in his stories the house was always a bright, happy place—big and rambling, yes, but full of light and laughter. What stood before me now was no refuge from monsters but a monster itself, staring down from its perch on the hill with vacant hunger. (3.116)
Jacob can't rationalize his grandfather's description of Miss Peregrine's house with the hollow shell it appears to be when he arrives there. It's practically the opposite of what Grandpa said.
"Sure, I remember them," he said. "Odd collection of people. We'd see them in town now and again—the children, sometimes their minder-woman, too—buying milk and medicine and what-have you. You'd say 'good morning' and they'd look the other way." (4.100)
The children of the home always seemed strange to the villagers, but not because they looked weird (they probably left the weirder-looking kids at home) but because they acted unusually.
"Let me see your eyes! […] No, your real eyes! Those fakes don't fool me any more than your ridiculous lie about Abe!" (5.122)
Emma wants to see Jacob's eyes because wights—some of the bad guys—don't have pupils. It seems that Emma knows that wights can alter their eyes, too, which makes it a little less surprising to learn that Dr. Golan hid his identity with contact lenses to make his eyes appear human.
Where had the townspeople been hiding all these big animals? Also, why was everyone looking at me? Every person I passed stared at me goggle-eyed, stopping whatever they were doing to rubberneck as I walked by. I must look as crazy as I feel. (5.81)
Jacob sticks out when he travels back in time because his clothes look so different than anything people wear in 1940.
"Of course he's Abraham Portman's grandson. Just look at him!" (6.29)
Jacob looks like his grandfather, which is nice because it helps Miss Peregrine identify him, but it's a little bittersweet for Emma, because Jacob's appearance reminds her of her love for his grandfather.
"I'm either one hundred seventeen or one hundred eighteen," said a heavy-lidded boy named Enoch. He looked no more than thirteen. (6.188)
Even though the kids are all basically senior citizens, none of them look that way. The time loops prevents them from aging.
"Nobody suspected a thing," [Emma] said. "People come to sideshows to see stunts and tricks and what-all, and as far as anybody knew that's exactly what we showed them." (7.37)
When most people see something that appears impossible, like a levitating person, they assume it's some sort of magic trick, not an actual supernatural power.
"Call me a dandy if you will, but just because the villagers won't remember what you wear doesn't give you license to dress like a vagabond!" (7.70)
We're not sure why Horace takes such pride in his appearance, but there's a nice photo to accompany his description in the book so you know exactly what he looks like.