We are having problems with multiple people contacting the same customer, or the wrong person contacting them, or one member of the team who should be notified about a customer's needs not being notified. What SaaS can we use to clarify this?
HelpScout, ZenDesk or Desk.com.
HelpScout (help desk software) would be a great start – less options but even when I ran a 6 person customer support team (with over 500 emails a day), we never needed the complex features of Desk.com.
Have one person create 'saved replies' to quickly answer your customers in a cohesive voice and with consistent responses. (However, encourage your entire team to inject some of their personality!) This seems like a huge task, but if they dig through their sent emails, it can be done pretty quickly.
Salesforce (Desk.com) could be the most feasible and one stop solution for your need. Let me know if you would like to evaluate the appropriateness of the platform per your need. I can help you around business problem definition, mapping it with right technology solution, and helping you adopt the technology with necessary customizations.
I have used Zendesk, Freshdesk and GrooveHQ. Zendesk scores the point because of its ease of use, its support, and an excellent knowledgebase platform to complement your support process. When you setup a help desk system, plan a few support articles in the Knowledgebase (Zendesk helps you here) to reduce the support calls.
I have helped business setup this support process, including the KB. Let me know if you need more details.