tl;dr there is at least one instance of a disorderly conduct charge for watching pornography in a public library.
I bring you the story of STATE OF WISCONSIN v DAVID J. REIDINGER. From the most recent (January 2016) appeals court decision:
David Reidinger was found to have violated WIS. ADMIN. CODE § UWS 18.11(2), which prohibits disorderly conduct in University of Wisconsin System buildings or on university lands. The evidence at trial
established that others witnessed Reidinger viewing pornography in a public library on the University of Wisconsin-Eau Claire (UWEC) campus. On appeal, Reidinger argues he has a First Amendment right to view legal adult pornographic material at a public library. Reidinger also vaguely alludes to a conspiracy between numerous public officers and employees to harass him. We reject these arguments and affirm.
Following a bench trial, Reidinger was found to have violated WIS.
ADMIN. CODE § UWS 18.11(2) and was fined $295. Shannon Riley, a student
supervisor at the McIntyre Library on the UWEC campus, testified she received a complaint from a student at 10:40 p.m. on December 14, 2014. The complaining student testified that she and her roommate were working on homework at the library when they noticed Reidinger watching pornographic material on the computer next to them. Two university police officers, Edward Lancour and Amanda Henry, responded to the complaint.
Lancour and Henry met with the complaining students, who showed
the officers a picture they had taken of Reidinger’s computer screen that showed open pornographic images. Lancour then personally observed Reidinger watching pornographic material on the computer for approximately thirty seconds before asking him to close the browser and move with him to a library stairwell to discuss the matter. Lancour testified he told Reidinger his watching pornography was causing a disturbance, to which Reidinger responded that he had a constitutional right to view pornographic material at a public library. Lancour then told him they
had received several complaints, and witnesses had stated that Reidinger viewing pornography at that location made them feel uncomfortable. Reidinger was issued a citation for disorderly conduct under WIS. ADMIN. CODE § UWS 18.11(2) the following day.
I am actually mildly surprised by this decision, because United States v. American Library Association, 539 U.S. 194 (2003) seems to indicate that the ability of adult users of a public library to disable Internet filters in order to view lawful content is constitutionally critical to the question of whether such filters are allowed, as stated in a concurring opinion by Justice Kennedy:
If, on the request of an adult user, a librarian will unblock filtered material or disable the Internet software filter without significant delay, there is little to this case.
Specifically, as stated in the dissenting opinion on Bradburn v. N. Cent. Reg'l Library Dist., 2010: "Even accepting for the moment that these libraries are not a limited public forum, eight justices found the ability of a patron to disable the filter constitutionally critical."
Thus there are many reports of libraries refusing to stop adult patrons from viewing pornography on these grounds:
However, a Washington State Supreme Court decision (Bradburn v. N. Cent. Reg'l Library Dist., 2010) found that public libraries do not have to disable Internet filters by request of an adult user.
(Note: I also posted this answer on Academia.SE)