We never see the evidence in a week or two of the abduction (and probable murder). We are given information during the manhunt because police desperately need help from the public. Now that he has been arrested, we probably won't get too much information. We won't know the evidence until there is a trial. Should we believe that he's innocent until the time of trial? Some may prefer to believe that he is a victim of police stupidity and incompetence, but I suspect that most will trust that police know what they are doing and they are well on their way to arresting the man for Hannah's murder (which of course is still not confirmed). The search for Hannah will continue, but we all know that if she is alive, she would have come forward. Jesse is in this alone ... there is no accomplice, per police.
The only reason that Jesse Matthew has been detained is because police now have evidence to suggest that he is responsible for her disappearance.
If direct evidence is required to trust police work, then best to check back in when the trial starts.