A crisp resume and interview are not conclusive indicators of a job candidate's true potential value - or lack thereof - to an organization. It's easy to get professional help to tighten resumes. Some manipulative people readily put on a professional face and charm and interviewer, later turning out to be a problem employee.
Talk is cheap and even seasoned HR pros can be fooled. Bad hires turn out to be among the most expensive, unfortunate business errors, even to the point of harming company reputations and bringing down organizations. As with many companies, we've certainly been fooled once or twice over the years, despite diligent vetting processes.
Luckily, easy screenings using public social media sometimes reveal a candidate's dirty face. Social media screens are suggested standard practice for any hire. Make sure to check with legal counsel to understand what employers may or may not consider and say about social media profiles, before and after an employee is hired.
Respect for Others
Twitter is a goldmine because most users' profiles are public. We can easily see a person's tweets, retweets, likes, and who they follow. It's easy to find a person's Twitter profile if she or he has one. Simply search Twitter and/or Google.
What does this Tweet say about a candidate?

As an employer, I care that people understand how their public behavior reflects on them. Particularly true when it comes to how they show respect for a client. The tweet above is painfully naïve at best. Easy to trace back, particularly with the reference to being a "good friend's DAD."
Precision and Pride
LinkedIn is a canary in a coal mine to for companies to screen the depth of an applicant's meticulousness. Portfolios may have been proofed and fixed by professors or friends. Anyone can hire a resume doctor to keep things from looking imprecise. However, not every applicant is sharp enough to make sure their LinkedIn profile is as crisp as their CV.

This guy's resume probably looks great but his LinkedIn profile indicates attention to detail might be an issue. "Mississipi" is actually spelled "Mississippi." Ouch. The individual is graduating from law school - entering a profession in which details matter.
Boundaries
Facebook offers users privacy controls to make sure personal matters can stay private. An applicant who chooses to publish highly personal content or shares posts that include workplace-inappropriate images or references to sensitive issues could be hinting they have boundary issues, in general. We've all seen questionable images in someone's Facebook feed - cringeworthy posts insensitive to human rights, diversity, women's issues and others. I DO know that sensitivity is crucial in matters of human rights. Questioning a candidate's boundaries based on such posts is reasonable.
Anger Issues
Often Twitter users behave with seeming indifference to the public nature of their own Tweets. Maybe a particular person consistently posts anger-filled rants on various topics - or even threats (veiled or overt) about politicians or other figureheads. Regardless of inspiration, if Twitter screening of applicants was the norm, would a person who willingly and consistently tweets f-bombs or outright threats against others EVER get hired?
Next time your company is hiring, don't forget to screen candidates' public social media profiles. Check Twitter, LinkedIn, Facebook, Pinterest, YouTube, Instagram and any other public threads. Other channels to check are pissedoffconsumer, AngiesList, Yelp, Google reviews and glassdoor.com because "reputation" can carry from when a candidate owned a business that sucked.
Other personal qualities to flag include narcissism, nudity, hate speech, violence, excessive profanity, bad grammar, inconsistencies in detailing credentials like education, previous employers and certifications.
Also germane is how an applicant speaks of previous employers. If they badmouth earlier jobs, brag about getting someone fired or note they've sued or been sued by former employers, take that as fair warning.
Important to note, the concepts discussed above also provide a clarion call to everyone using social media to realize job screenings and interviews can, and will, extend beyond the face-to-face interaction. Things said or posted in public channels can and will be used in the court of hiring opinion.