Asking for a candidate's social media password is illegal in seven states*, and generally frowned upon (by job seekers at least) in most others. But if you feel like you need to obtain a password to view their social profiles, then chances are you probably wouldn't "dig up" anything anyway.
Listen, most millennial job seekers aren't naive when it comes to social media. When Facebook first launched in 2004, teachers began warning their students to not post anything risque or illegal because it could jeopardize one's chances of being accepted to college. Nearly 10 years later, we're hearing the same thing - don't post something you wouldn't want potential employers to see. Well guess what, today we live our lives on Facebook and Twitter, and while we would prefer for potential employers not to see our pictures and posts, that's not going to stop us from posting anything.
There's a way around all those security settings, and if you're willing to go that far as an employer, you may need to reevaluate your hiring process. Sure, the person you are meeting in an interview is different from the person who went on a bar crawl last weekend. But does that matter? Of course your employees are representing your company at all times, but if who they are outside of the office doesn't impact their quality of work, then so what if they are a regular at the local karaoke bar (unless they're a bad singer, then an intervention is called for).
There are exceptions to this, but generally speaking it's not fair (and sometimes illegal) to base a hiring decision off a candidate's social media profile. If they interviewed well and have the experience you're looking for, then their tweets really shouldn't matter. But if you're still questioning whether you should hire them even after they blew you away during the interview, you may want to reconsider the questions your asking. When you're reviewing your notes from each interview and looking at the scores, you should feel confident knowing which candidate you want to extend an offer letter to without having to examine their social media accounts first.
Instead, try conducting a reference check. You'll likely to get an honest answer from the candidate's past employers and will be able to better determine whether they're a fit for your company.
*These states include California, Delaware, Illinois, Maryland, Michigan, New Jersey, and Washington.