Obviously, modern technology such as computers and mobile phones did not exist in ancient Roman times. In order to answer this question, I am working on the hypothetical premise that the Romans did have access to social media through mobile phones and computers. However, to avoid confusion and inference between the advantages of technology and the advantages of social media, I am also working on the premise that mobile phones and computers were exclusively used to access social media, they would not have been used for any other purpose.
One aspect where life could have improved during ancient Roman times through the use of social media is very easy to see: communication between people who were not at the same geographical location. Instead of sending a messenger with a message, which was common practice in ancient Rome, Romans could have simply sent a message on social media, thus saving precious time. Depending on the distance, this could have saved hours, days, or even weeks in order to pass on an important message.
Another aspect of life that could have improved is the treatment of slaves. Nowadays, people who feel treated unfairly or discriminated against can find a way to communicate with each other through social media. They can also raise more attention to their situation through publicizing information online and demanding fair and equal treatment, like the LGBTQ community. Had the slaves had this resource in ancient Roman times, perhaps this could have led to a drastic improvement of their conditions, if not even to the abolition of slavery itself.
Social media would have also been very useful for trade. Merchants in ancient Rome mostly relied on word of mouth in terms of advertising. However, had they had access to social media, they could have advertised their goods through social media and therefore attracted more potential buyers. Also, customers could have left customer reviews through social media. In this way, recommendations would have spread to a far bigger audience and would have been far more effective as advertisement.