Al-Ḥāfiẓ Ibn Kathīr, Ibn Qayyim and other than them sometimes mentioned aḥādīth without paying much attention to their authenticity, and perhaps this is because of either two reasons: 1. There are other aḥādīth that strengthens that ḥadīth or 2. It is a ḥadīth that encourages the good or admonishes against the evil, and therefore there is certain amount of leeway that can be taken with regards to them.
The manāhij (methodologies) of the muḥadithīn (scholars of ḥadīth)
The four sunan (Abū Dāwūd, At-Tirmidhī, An-Nasaa’ee, and Ibn Majah), the musnad of Imām Aḥmad, and the sunan of Ad-Dārimī, all contain aḥādīth that are ṣaḥīḥ (authentic), ḥasan (good), and dāʿīf (weak). For they did not make it a condition for their books to contain only the aḥādīth that are ṣaḥīḥ as Al-Bukhārī and Muslim did. Rather, their intent was to gather all the aḥādīth as they relate to a particular matter. Similarly are those other such the musnad of At-Taylasee and the three maʿajim of al-Tabarānī. As for the muwaṭṭaʾ of Imām Mālik, it contains aḥādīth that are ṣaḥīḥ, ḥasan, and dāʿīf.