Channeltivity integrates with your Salesforce.com account through the Salesforce.com webservices API. Channeltivity's integration with Salesforce is fairly conservative with its usage of the Salesforce API and you shouldn't run into any limits. However, if you have other applications that make extensive use the Salesforce API, you may run into the Salesforce REQUEST_LIMIT_EXCEEDED error.
How to check your Salesforce API Usage in Channeltivity:
Go to the Salesforce Sync Manager Page (Settings > Salesforce Integration > Sync Manager) and you'll see the Salesforce API calls made by Channeltivity in the last 24 hours:
How to check your API Usage in Salesforce:
Step 2: Click on the "Company Information" link under "Administration Setup" and "Company Profile" in the side navigation:
Note: if you don't see the API Requests number, it could be because your Salesforce instance doesn't have the API enabled. Only Salesforce Enterprise Edition includes the API by default. Salesforce Group and Professional Edition don't include the API, although you can pay to get API access with Professional Edition.
If you're looking for more detailed reporting on your Salesforce API usage, here's an article that explains how to Export Salesforce Event Logs for viewing.