Do the saheeh collections of ibn Hibbaan and Al-Mustadrak of Imaam Al-Haakim contain any weak narrations?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

Yes, there are indeed weak narrations in Saheeh Ibn Hibbaan and in the Mustadrak of Al-Haakim . That is because Ibn Hibbaan did not restrict his narrations to trustworthy narrators; rather sometimes he may narrate from unknown people.

As regards Al-Haakim he is even more lenient than Ibn Hibbaan. His book Al-Mustadrak contains even some fabricated narrations. Ath-Thahabi critiqued many of the narrations reported by him. For more benefit, please refer to Sharh-As-Sakhaawi Li-Alfiyyatul-'Iraaqi. 

Moreover, many narrations, which Ibn Hibbaan reported in his book, and which Al-Haakim reported in Al-Mustadrak, were classified by Shaykh Al-Albaani as weak. In addition, in the critique of Ath-Thahabi on Al-Mustadrak of Al-Haakim, Ath-Thahabi, opposed Al-Haakim in many cases, in his judgment about the narrations that he classified as authentic.

Allaah Knows best.