The evidence that is and is not accepted might seem to us, these days, a bit backwards. Every single piece of logical, sensical, confirmable evidence is rejected, while any displays of hysteria, acting and theatrics from the girls is.
Rejected evidence: A petition of close to 100 people attesting to the righteous nature of the accused women (all 100 arrested for questioning); a statement from Corey who had a witness who heard Thomas Putnam say he was "killing his neighbors for their land" (Corey is arrested); Mary Warren's claim that the girls are faking their hysterics to cover their own skins over the dancing incident (Mary is harassed and questioned and commanded to faint instead); and Proctor's assertion that Abigail is an adulteress (not believed because Elizabeth understandably lied to cover her husband's reputation).
Accepted "evidence": Abigail's hysterical assertion that Mary was a yellow bird who, filled with envy over Abby's beauty, had come to tear her eyes out; Mary's quick turn-around to accuse John of being "the Devil's man," even though she was on his side but minutes before.
As you can see, the tables seem to be a bit turned on what we might deem acceptable evidence today. Why were they so ridiculous? Well, they'd already convicted hundreds of people of witchcraft; to listen to the rational evidence would prove that they had accused those people wrongly. That would ruin the judge's reputations forever. If the judges were known to have erroneously charged hundreds of people with witchcraft, because of the antics of some silly girls, they would be ruined. Also, the hysterics are much more dramatic, intense, and bizarre--it's almost impossible to believe the girls would knowingly behave in such ways, knowing that they were sending innocent people to their deaths. The improbability and their naive trust in the girls, along with their own desire to protect their reputations, kept the judges from accepting more rational evidence in the courts. I hope that helped; good luck.