Verification is a feature common to Facebook, Twitter and several other social media networks. The problem it was created to solve was to differentiate between Jan Smith the famous actor and Jan Smith, the absolute nobody who wants to build social capital off the reputation of Jan Smith. Or indeed, to attempt to sully the social reputation of Jan Smith.
All the "real" Jan Smith needs to do is provide proof of identity and their username, and the networks will add a reassuring "tick" to let everyone know who is real and who is not.
Twitter is one of the few networks that still allows anonymous and parody accounts to be created, so I believe the risk of confusion and impersonation is greater.
As with basically every other feature ever, the problem is more complex than it first appears.
The "blue tick" is now seen as an endorsement. This mixes the reputation of the network with the reputation of the verified user. Additionally, since it appears to be an endorsement, and is of limited availability, the award of the blue tick is greatly prized. There is always someone in my DMs asking if I can help them get verified (I cannot).
Once a user has a blue tick confirming their identity, what does that mean? Can they then change their photo, their name, their username, their bio? And if they do, what does the tick mean?
In a world of seven billion individuals, who gets to decide who the "real" Jan Smith is? How does Smith apply for verification? What if a Jan Smith has already been approved for verification? What if the individual lives in a place where they do not have a way to prove their identity (a surprisingly common issue)?
Verification is a combination of identity (proving that your name is what you say it is), and credibility (showing which person with that name you are).
If I were to try to define such a system, I imagine I would try to build my qualification criteria off existing systems. Perhaps I'd leverage passports, government ids, and credit cards for identity. And for a measure of credibility I'd look to large reputable organisations like newspapers (for journalists), sports teams, religious institutions, elected government officials, and so forth. Beyond those, I'd try to establish a measure of credibility in their field, based on mentions in the press, or wikipedia.
Without a measure of credibility, we might be asked to verify every single "Jan Smith", which would undermine our solution to the original problem: how do I find "my" Jan Smith?
The trouble with mesuring credibility based on external factors is that we will accumulate all the biases of the original sources. If men are more likely to get published in the press, and more likely to apply for verification, they're doubly likely to be approved.
Have a think about how we could qualify the credibility of someone in their field. Perhaps you would base it on the approvals of a given amount of other network users? LinkedIn does that for "skills". But that factor could easily be abused; you'd need to account for that in your model. And remember the seven billion people problem: we can't employ a private investigator for each and every applicant. It's a difficult problem.
In my opinion the best solution (not my idea, widely discussed already), is to split the confusion of identity verification and endorsement of credibility. Identity verification should be widely available, and networks could even tell us which method they used, eg "Facebook has seen copy of US Drivers License".
Endorsement of credibility should still be left to others. Allow people to link to official websites and crawl those websites for usernames to be verified. When approved, add the website to the user's profile. This means the networks need only vet official websites for validity. Obviously this is still not trivial, but might be more managable.
This takes time and resources, both of which are carefully managed at any social network, regardless of size. I don't expect to see it fixed soon.
One final problem to consider appeared last year. My friend contacted me on behalf of @dog_rates, asking if I could help with verification (I couldn't). There were plenty of impersonating accounts, so I can see why it makes sense. But how do you verify a user without an identity?