* Potential marketing for your startup, especially if you gain followers that are also in your target audience.
* Have a way for someone (e.g. investor, potential employee, potential business partner, etc) to look you up and see what kind of person you might be.
CONS
* Distraction away from your customers and team, which should be among your top priorities. It can take time to cultivate a social media presence.
* Misinterpretation risk. For better or worse, if you happen to say something that can be misinterpreted, and someone has an agenda against you, social media can be risky. Assume that everything you say can be posted on a billboard in every major city.
MY $0.02
Each of these carry different weights. I would argue that the disadvantages far outweigh the advantages.
If you want marketing benefits, you'll get more bang for your buck by having someone with lots of marketing experience. Being discoverable by investors via social media is really a minor thing; you'd have to substantially invest in your "social media reputation" in order for this to give you anything, and even then, it's more useful as a tool to maybe get meeting with an investor, than it is to secure funding from that investor.
Being a distraction from your core priorities is really the most important thing I'd offer. Social media can easily be a black hole for attention and time. That's attention and time you can't afford to lose right now.
When I removed Twitter, I found that there was definitely a missing piece of my outreach to the community. If you use Twitter effectively, it can help build your personal brand which, in turn, can help your company's brand.
Just don't let it turn into mindless surfing. Keep your activity tactical with a marketing objective. The goal is to add value to your business in terms of hiring and technical influence.
Unless you are producing lots of marketing materials (tutorials, new features, blog posts, etc) and/or creating an audience I don't think you should invest resources in being active. A simple light presence should be enough.
Lots of people (myself included) prefer to send a tweet to a project/company than sending an email. This has the advantage that it's a public indexable conversation that could, given the circumstances, even become viral.
This. I'll tweet-complain at a company but I'm not going to mess with opening up a customer service chat or firing off a customer service email where I may or may not get someone based in the United States and might have to wait several minutes with a chat to get someone or a day or more via email.
If a company has a decent customer service plan, they're usually pretty on top of seeing twitter mentions and will reach out. AT&T, Zappos, McDonalds, State Farm, WEMO, Wendy's, Papa John's, Chevy Customer Care and Bumble are just some of the companies I've had positive exchanges with on Twitter when I've had issues.
Companies I've taken useful information from their posts however is considerably smaller: the Red Dwarf account (how I learned about the most recent season).