The majority of Muslims agree on the authenticity of all hadiths reported by both al-Bukhari and Muslim. This commenced in the first era of Islam, especially after the golden era of tadwin (compiling and writing down the hadiths) in the third and fourth centuries after Hijrah. They consider their two Sahihs the most reliable and authenticated sources of hadith.
Though having confidence in their authenticity, Muslim scholars pursue a scientific methodology and scrupulous verification when quoting them. It is reported that some Hadith scholars had criticized a few sahih or sound hadiths. Others, moreover, differed among themselves if certain hadiths mentioned in the two Sahihs adequately met the conditions stipulated by al-Bukhari and Muslim. Their discussion, however, did not reach the level of weakening the hadiths reported therein.
the Muslim methodology of reviewing, verifying, and checking the minute details (e.g. the orthography and the vocalization of the text, the reliability of the narrators, etc) indicates that the science of Hadith matured to a stage not witnessed by other civilizations. As evidence of this, one thousand years ago, the Muslim library had biographies of at least 100,000 Hadith narrators. These biographies helped identify the reliability of a certain narrator. Also the voluminous works of that science is still within our reach, helping us sort out the good, the sound, and the weak among the hadiths of our beloved Prophet Muhammad (peace and blessings be upon him).