What are some examples of passages which demonstrate Bromden's tendency to hallucinate or exhibit paranoia in One Flew Over the Cuckoo's Nest?

It is important to recognize that Kesey never explicitly states within One Flew Over the Cuckoo's Nest that Bromden is a paranoid schizophrenic, and as such, as readers and interpreters of literature, we can only speculate on what his diagnosis might be. That said, Bromden is an intensely paranoid individual and experiences hallucinations frequently in the text. We can look to his overwhelming fear of the Combine (and the conviction that it exists), as an instance of paranoia. Consider, for example, his insistence that Nurse Ratched works as an agent of the Combine:

So she works with an eye to adjusting the Outside world too. Working alongside others like her who I call the “Combine,” which is a huge organization that aims to adjust the Outside as well as she has the Inside, has made her a real veteran at adjusting things. She was already the Big Nurse in the old place when I came in from the Outside so long back, and she’d been dedicating herself to adjustment for God knows how long (Kesey 19).

In this excerpt, Bromden claims that Ratched has the ability to manipulate and distort reality both inside and outside the ward, "adjusting" it periodically because she works for the ominous Combine. Indeed, Bromden believes that Ratched and the ward staff are capable of subduing and disorienting him by emitting a "fog" on the ward (Kesey 9). One interpretation of the fog is that that Bromden is being sedated, which could cause a strong sense of lapsed time and confusion. 

In terms of hallucinations, we see early in the novel that Bromden's observations and personal accounts signal that not all of his experiences are actually happening. For instance, as the fog rolls into the ward, Bromden describes Nurse Ratched's actions as such:

I can’t see six inches in front of me through the fog and the only thing I can hear over the wail I’m making is the Big Nurse whoop and charge up the hall while she crashes patients outta her way with that wicker bag. I hear her coming but I still can’t hush my hollering. I holler till she gets there. They hold me down while she jams wicker bag and all into my mouth and shoves it down with a mop handle (Kesey 9). 

Nurse Ratched does not truly shove a wicker bag down Bromden's throat with a mop handle, clearly, but in this example we see that Bromden's hallucinations occasionally expose a deep fear of violence or harm done toward him. Nurse Ratched, as a figure of power and authority on the ward, is frequently seen as a threatening force within the novel. In the above passage, we see how the perceived threat of Ratched becomes an imagined threat of violence toward Bromden, which he experiences as a hallucination. Because Bromden is the narrator of One Flew Over the Cuckoo's Nest, we must evaluate the reliability of his account of the ward, and frequently we find that what Bromden describes throughout most of Kesey's novel cannot and is not really occurring.  

Source: Kesey, Ken. One Flew Over the Cuckoo’s Nest. New York: Signet Books, 1962.