There are two ways in which Clarisse makes Montag feel uneasy.
First, she makes him feel she is judging him:
He felt she was walking in a circle about him, turning him end for end, shaking him quietly, and emptying his pockets, without once moving herself.
These words demonstrate that Montag felt looked at from every angle. He felt as if the items he might have had with him were being evaluated. Perhaps he felt this way just because of Clarisse's eye for detail. She knew how to notice.
Next, she proves that she thinks... a lot. After asking questions about firemen putting out fires instead of starting them, and if he ever reads books, Bradbury narrates:
"You think too many things," said Montag, uneasily.
Montag is growing uncomfortable with her ability to think. He isn't used to it.
Finally, she questions his happiness. This causes him to think:
Of course I'm happy. What does she think? I'm not? he asked the quiet rooms.These words are obvious signs of uneasiness. He is beginning to question himself.