1. Match your in-person experiences to your online image. With many banking activities being conducted online these days, customers and members are visiting branches less frequently. But that doesn't mean institutions should slack off when it comes to in-person service.

Moyer pointed out bank customers typically reserve their branch visits for making their most important decisions, so it's more important than ever to provide great service in those instances. If an institution presents a glowing image of itself on its Facebook page but offers crummy service in person, the customer will be displeased – and likely to let the world know about it, too.

"If a customer has a bad experience in a branch, they're going to tweet about it," she said. "Focus on aligning your social media strategy with the experience you deliver in the branch."

2. Invest in mobile. Financial institutions might consider spending more money on improving their customers' or members' experiences when visiting their websites or social media pages on mobile devices, Canning suggested. Citing eMarketer research, he noted mobile currently comprises 24% of U.S. consumers' total media consumption. However, according to the International Data Corporation's Media Market Model, of the approximately $632 billion spent by companies on marketing, only about $16 billion (or less than 3%) is devoted to mobile, he said.  

"There's a good opportunity here for financial institutions to move fast on mobile and not let their size be an inhibitor," he said.

3. Humanize your institution. The Kansas City, Mo.-based Lead Bank recently donated a horse to its local police department and chronicled the experience on its Facebook page, Rowland explained. The bank's Facebook fans commented on posts about the horse's training sessions and even posted selfies with the horse (named "Leader") when they spotted it around town. In exchange, the bank had the chance to promote the local police and agriculture departments and associate its brand with them as well.

"The response to the campaign was fantastic, and it reflected well on us," Rowland said. "It created a halo around us and around Kansas City, and we were able to create the 'What are we here for?' story."

4. Focus on engagement, not advertising. "Advertising is expensive and useless today – engagement is much more important," Rowland asserted. The other panelists agreed, stating that instead of buying ads online, financial institutions should focus on having meaningful online interactions with their current and potential members or customers.

The Harrisburg, Penn.-based Centric Bank, for example, uses its social media accounts to share positive community news, promote events such as educational luncheons and give shout-outs to clients when they receive awards or other recognitions, Husic said.

5. Leverage social media in a crisis. When a natural disaster leads to service interruptions or a system conversion goes awry, a financial institution's customers or members are likely to share their questions and complaints on social media. That means it's crucial to actively communicate via social media platforms when a crisis occurs.  

During Hurricane Sandy, Centric Bank took to Twitter and Facebook to share the status of branch closures, ATM outages and payroll deposits, for example, Husic said. As a result, the bank successfully mitigated its reputational risk and gained the trust of its customers.

Canning added, "There's a conversation going on [online], and the question is, do you want to participate in it, help steer it, or let it run rampant? Our advice is to jump right in."