Salesforce has announced their "Insufficient Privileges" issue has been resolved as of July 12th 4:08 pm PDT.
As a result, DialSource should also be up and running normally.
Salesforce has announced on their https://status.salesforce.com site of an issue at this time on their side of things.
The issue at hand will affect DialSource Users when they attempt to call and disposition records. Users may not see their calls log properly, and as a result other post-call automation will not be triggered as well.
You may also see other Salesforce functionality affected at this time.
We believe once Salesforce resolves their issue, DialSource functionality will resume as normal.