The New Account button has been updated as part of Luminate CRM version 12.9.

Here are the steps to resolve this error:
  1. Click on Setup > Customize > Accounts > Buttons, Links and Actions
  2. Click Edit next to the New label
  3. Choose Visualforce Page
  4. Choose Account Dupe Check [cv__Account_Dupe_Check]
  5. Click Save
However, each administrator profile will need to have access to the Visualforce page that now powers the button.  This will need be updated if an admin is now getting the error "Content cannot be displayed: You do not have sufficient privileges to access the controller."

Here are the steps to update the Visualforce page permissions:
  1. Navigate to Setup > Manage Users > Profiles
  2. Click the name of the profile
  3. Click Enabled Visualforce Page Access > Click Edit
  4. Move cv.Account_Dupe_Check from the left box (Available) to the right box (Enabled)
  5. Click Save
UPDATE: 2/12/2015:

This issue can also happen when trying to create new Campaigns. To fix, follow these steps:
  1. Navigate to Setup > Manage Users > Profiles
  2. Click the name of the profile
  3. Click Enabled Visualforce Page Access > Click Edit
  4. Move cv.CampaignCreateButton from the left box (Available) to the right box (Enabled)
  5. Click Save