Interim CEO Jack Dorsey before he grew out an awesome beard. Source: David Shankbone

With the era of Dick Costolo coming to a sudden close at Twitter (NYSE:TWTR), its board is charged with finding a replacement who can take charge of a company that has often failed to live up to its potential. In the interim, co-founder and former CEO Jack Dorsey will take over the role once again, but says he's not interested in leaving his position as CEO of Square, which he founded after leaving Twitter. Giving up that post at Square would be a prerequisite for Dorsey to take the job at Twitter permanently.

If Twitter is to succeed following Dick Costolo's departure, there are three key areas where the company's next CEO needs experience: running a public company, growing an advertising base, and product design and positioning. Let's take a look at all three.

Experience running a publicly traded company
While rumors have it Twitter is reviewing several internal candidates including CFO Anthony Noto and President of Global Revenue Adam Bain, no one on Twitter's management team has any experience running a publicly traded company. That's important because answering to public shareholders is much different from answering to private equity investors.

A private company is able to take a long-term view and can easily ignore critics. A publicly traded company must face its critics and convince people to stay the course and not be discouraged by short-term setbacks. This is something Twitter failed to do well under Dick Costolo. As early investor Chris Sacca put it, management has failed to "tell its own story."

It's not that Costolo and his team lacked a vision -- the number and concentration of new product features rolling out this year are proof of that -- he just failed to communicate and convince investors that the company is on track to achieve that vision. Someone with experience running a publicly traded company may have handled last quarter's huge underperformance differently, showing how it's going to improve on its missteps with direct-response advertising instead of simply saying it will.

A CEO needs to instill confidence not just in his team but in the public as well, and that's an area where Dick Costolo didn't always succeed.

An advertising guru
The reason Adam Bain is getting a lot of attention is because he has proven quite capable of building Twitter's ad business. He joined Twitter in 2010 and took Twitter's ad business from $0 to what's expected to be $2 billion in just six years. Previously, he helped monetize News Corp's web properties while working at Fox Audience Network.

Indeed, advertising is essential to Twitter. Last year, ad revenue accounted for nearly 90% of the company's total revenue, an increase from 85% in 2012. Finding someone capable of growing that revenue source is key, especially in light of the recent shortcomings with the switch to direct-response advertisements.

Finding someone with experience growing an ad business, particularly one with lots of smaller businesses like Google or Facebook, will provide Twitter with a strong foundation to continue growing beyond simply increasing the ad load in users' timelines.

A product genius
To be fair, Twitter already has a couple of product geniuses working for the company, namely Kevin Weil and Alex Roetter, who took over as VP of Product and VP of Engineering, respectively, last fall. Their work is evidenced by the acceleration of new product features Twitter has rolled out in 2015 such as its revamped logged-out homepage and native video capturing. Previously, the VP of Product had been a revolving door since Jason Goldman left in 2011.

Twitter needs someone that can work to get the most out of Twitter as a communication and content platform. It's an area Twitter spent years lagging behind the competition, but it's finally started to pick up steam in the last year with the help from Weil and Roetter.

Stand-alone product acquisitions like Periscope and technology acquisitions used to improve on existing Twitter products like Whetlab is the biggest area the future CEO could have an impact. Someone a knack for massive consumer facing products, and an understanding of the strategic pieces that need to come together in order to deliver that vision is what Twitter needs in a leader.

Bonus points if he or she knows how to use Twitter
Amazingly, Twitter's management has had a lot of trouble using its own product. Anthony Noto famously confirmed that it should make an offer to acquire some unnamed company through a public tweet that was meant to be a direct message. Just recently, Kevin Weil -- the product guy! -- errantly sent a tweet that was intended to be a direct message as well. All told, just four of Twitter's top 11 execs tweet very often at all.

Someone with intimate knowledge of the product is going to have better ideas for how users use Twitter and how it can improve the product and advertising business. Ultimately, that's what's going to provide better results for Twitter going forward.