The book at-Targheeb wat-Tarheeb of Hafidh al-Mundhiree is a good book but his selection of authentic Hadiths are not to the level of Riyaadh us-Saaliheen. Since Riyaadh us-Saaliheen of an-Nawawee is more refined in Hadith than it.
As for the book at-Targheeb wat-Tarheeb then in it are Hadiths which are weak (Da'eef), and it has terminology which is particular to it, that is when he mentions at the beginning of the Hadith Ruwiya (it has been reported) or Hukiya (it has been mentioned) or a form from the forms of Tamreedh the passive verb form [where the subject of the sentence is unnamed], then that indeed is an indication of the Hadith being weak (Da’eef) and al-Mundhiree refers to this terminology in his introduction.
It also has another terminology, which is, when he mentions a narrator or two narrators from the Sanad (chain of narration) before the companion then it is known that the Sanad (chain of narration) has some weakness (D’af) in it with regards to the narrator or the two narrators which he has mentioned from the Sanad (chain).
Al-Haafidh al-Mundhiree has given a biography of each one of those narrators whom he has mentioned and he speaks regarding them at the end of the book. So with this then al-Mundhiree rahimahullaah is excused for that which he mentions from the Hadiths. That is since he has clarified the grade of majority of them and the condition of the narrators that have been spoken about [i.e. disparaged]. Then what remains is your role, either you accept the Hadith or you do not accept it. But the ruling upon the Hadith from the point of view of the terminologies that al-Mundhiree has employed is in need of expertise in this subject matter, so whoever finds in himself this expertise then there is no harm in him reading the book at-Targheeb and benefiting from that which it contains. As for the one who sees that he does not have the likes of this expertise then it is better for him that he reads from the book Riyaadh us-Saaliheen of an-Nawawee; since it is more refined in Hadith from at-Targheeb wat-Tarheeb and is more clear in its approach and methodology.
And Allaah knows best and may the peace and blessings of Allaah be upon His servant and His Messenger Muhammad.