In 1987, Rao and his team published a series of four papers, of which three were in the Proceedings of the Indian Academy of Sciences (Chemical Science), Pramana, and Current Science, all published by the Indian Academy of Sciences. A report was submitted to the Society for Scientific Values that the three papers had no mention of the dates of receipt, which were normally explicitly mentioned in those journals. Upon inquiry, it was found that the paper manuscripts were actually received after the date of publication, indicating that they were backdated. The society declared the case as "Use of Wrong Means to Claim Priority."
Rao has been subject of allegations on plagiarism. Rao and Saluru Baba Krupanidhi at the Indian Institute of Science in Bangalore, with their students Basant Chitara and L. S. Panchakarla, published a paper "Infrared photodetectors based on reduced graphene oxide and graphene nanoribbons" in the journal Advanced Materials in 2011. After publication the journal editors found sentences copied verbatim in the introduction and methodology from a paper published in Applied Physics Letters in 2010. According to Nature report, it was Basant Chitara, a PhD student at IISc, who wrote the text. An apology was issued by the authors later in the same journal. Rao said that he did read the manuscript and that it was an oversight on his part as he focused mainly on the results and discussion.
Scientists such as Rahul Siddharthan (Institute of Mathematical Sciences, Chennai), Y.B. Srinivas (Institute of Wood Science and Technology), and D.P. Sengupta (former professor at IISC), agreed that the plagiarised portion has no bearing on the findings, yet Siddharthan opined that the reactions made by Rao and Krupanidhi were overboard. Rao and Krupanidhi publicly blamed Chitara, and denied the publication as not plagiarism. Rao had commented, "This should not be really considered as plagiarism, but an instance of copying of a few sentences in the text." He even extended the blame to Krupanidhi asserting that he had no role in it as it was written by Krupanidhi without his knowledge. His claims were not justified by the fact that he was the senior scientist and corresponding author in that publication.
More allegations of instances of plagiarism in articles co-authored Rao have been reported. Written with S. Venkataprasad Bhat and Krupanidhi, Raos paper in 2010 about the effect of nanoparticles on solar cells in Applied Physics Express contains texts that are very similar to those of a paper by Matheu et al. from Applied Physics Letters in 2008, which it did not even cite. Rao had stated, referring to the 2011 incident, that "[If] I have ever stolen an idea or a result (in) my entire life, (then) hang me." But Raos article contains similar study to and duplicated figures with that of Matheu et al. An article in the Journal of Luminescence in 2011, written with Chitara, Nidhi Lal and Krupanidhi, contains 20 unattributed lines which appear to be copied from articles by Itskos et al. in Nanotechnology (June 2009 issue) and Heliotis et al. in Advanced Materials (January 2006 issue). Another article in Nanotechnology, written also with Chitara and Krupanidhi, uses six lines from the 1995 article by Huang et al. in Applied Physics Letters.
Rao was given a Bharat Ratna by the Government of India in spite of the controversy and was active as a professor at Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR). In December 2013, brother and sister Tanaya Thakur, a law student, and Aditya Thakur, a class XII student, filed a public interest litigation in Allahabad High Court, Lucknow Bench, to challenge Rao's Bharat Ratna. They asserted that "a scientist with proven cases of plagiarism shall not be presented the highest civilian award." But the court ruled them out as "filing pleas for publicity." There was another plea to revoke the award in 2015, but the Central Information Commission dismissed the petition.
On 17 November 2013, at a press conference following the announcement of his Bharat Ratna, he called the Indian politicians "idiots" which caused a national outrage. He said, "Why the hell have these idiots [politicians] given so little to us despite what we have done? For the money that the government has given us we [scientists] have done much more." In his defence Rao insisted that he merely talked about the "idiotic" way the politicians ignore investments for research funding in science.