I shared a dashboard with another user but they're getting an "access denied" message.

When sharing a Dashboard with another user, does that user have to be in an analytics user group that have permissions to access those widgets, location, etc that are in the dashboard being shared?

Yes, the person you are sharing the dashboard with must have the appropriate rights in Analytics to view the widgets and data that is being shared with them. The exception to that is when you email a dashboard or publish a dashboard to the web.