Asalaamu Alaikum wr wb, In fact many of the great hadith collections contain weak hadiths. This is the case with Sunan al-Tirmidhi, Ibn Maja, al-Bayhaqi, al-Mustadrak of Imam Hakim, Mishkat al-Masabih, al-Tarqhib wa al-tarhib, etc. Besides these, popular works such as the Ihya 'ulum al-din of Imam Ghazali is one in which Allama ‘Iraqi has judged many hadiths to be weak. However, these works have been overwhelmingly accepted by the majority of traditional scholars of Islam throughout the centuries. Furthermore, despite the rigorous authentication of the Sahih of Imam Bukhari, his other works such as al-Adab al-Mufrad and Juz’ al-qira’a khalf al-imam contains many weak narrations.
What we understand from this is that it is not a crime to relate weak hadiths, as some like to advocate. Individuals have risen in the last century who have attempted to “purify” the books of the pious predecessors by sifting the weak hadiths from the authentic (many a time with great injustice) and have published the classical collection under new titles such as Sahih Sunan al-Tirmidhi, Sahih Sunan Ibn Maja, etc.
The approach of the classical scholars was not such. It was accepted among them that works on the subject of virtues and fada’il did not have to meet the same levels of authenticity as was needed in discussions on the belief system of Islam or the laws and rulings of the lawful and unlawful.
Great hadith experts such as Imam Ahmad ibn Hanbal, Ibn al-Mahdi, 'Abdullah ibn al-Mubarak said, "When we narrate in regards to the lawful [halal] and unlawful [haram] we exercise extreme strictness and when we narrate in regards to virtuous and the like (stories and narratives) then we are more lenient. (See Suyuti’s Tadrib al-rawi).
We learn from this statement that the scholars were more relaxed in the case of using weak hadith in virtues, but were very strict when it came to aspects of belief or fiqhi rulings. There were also other conditions for accepting weak hadith. For instance, the weakness should not be extreme that it is bordering on fabrication or the hadith should not be a spurious one. Likewise the weak hadith should not contradict an established principle of Shari’a or go against the spirit of the teachings of Islam (See Tadrib al-rawi).
If one takes the approach of shunning every book that contains weak hadiths would be left with very few books to benefit from. This would create great difficulty in regard to the din. Imam Tirmidhi has demonstrated in his Sunan as to how so many fiqhi rulings have been based on not-so-strong narrations.
Source: http://qa.sunnipath.com/issue_view.asp?HD=1&ID=1818&CATE=91