The first evidence that Proctor brings forth is the petition that nearly 100 people signed, attesting to the righteous character of the women in jail. Danforth questions that evidence because, prompted by Parris and Hathorne, those people themselves might be under the influence of some evil force, if they were to question the authority of the courts. It upsets Danforth that so many people would question his rulings of witchcraft--his pride is injured, and he will not be made a fool of. So, he orders all the people that signed the petition to be arrested for questioning.
The second evidence that Proctor himself brings forth is that of Mary Warren, who testifies that the girls are faking. He questions that evidence because Mary Warren, when commanded to faint, cannot faint--this seems to prove to him that she was indeed bewitched at the time of the accusations. Also, Abigail starts claiming Mary's spirit is attacking her, and Mary chickens out and blames Proctor, calling him a witch.
Lastly, and most significantly, Proctor claims that Abigail is a whore, and then he confesses that he committed adultery with her; as a result, Abby contrived to accuse Elizabeth, in order to "take her place" by his side, as his wife. Danforth questions this evidence for a couple reasons. First of all, Abigail denies the affair. Secondly, he brings in Elizabeth and asks her straight-out if her husband is a lecher (adulterer). Elizabeth, in an understandable lie, denies that John commited lechery, and so disproves any claim that John had in regards to the issue.
Underlying all of his doubts though is Danforth's claim that John has come to "undermine the courts." He thinks that Proctor not only wants to save his wife, but also to prove every conviction that Danforth has made false. This would ruin Danforth's reputation--if John can prove that the women are innocent, and Danforth was the one to condemn them to death, Danforth's career will be over. He will forever be known as the guy who falsely convicted many people to die, and that will be the end of him. So the main reason he thwarts John's attempts is to keep John from undermining his precious authority in the courts, in order to protect his reputation.
I hope that those thoughts helped; good luck!