Part A: Identify the conflicting custom field
You must scour every field in both the Contact and Account objects for a possible suspect.

To do this:
  1. Click your name at the top.
  2. Select Setup.
  3. On the left side under App Setup, select Customize > Accounts *[Contacts] > Fields.
  4. Scroll down to the custom fields.
  5. Examine the custom fields for any with the data type of Contacts(Lookup) *[Accounts(Lookup)].
  6. When you find one, cross-examine with the standard and custom fields that exist and identify a potential duplicate by comparing the internal field names.
For example:
Account Custom Field:
Public Name: Org Proxy Contact
API Name: Contact__c
Data Type: Lookup
The issue is that this account custom field is having to perform a lookup of a contact field with the name of Contact__c. However, this directly conflicts with a field that is labeled as cv__Contact__c (Public Name is Contact). While they look different, Salesforce has trouble recognizing the difference, because what is inside the underscores is the same.

*If you do not find a field in the Accounts object, then switch over and peruse the Contacts object.

Part B: Adjusting the custom field
After identifying the field, change the internal name to something else, something more customized that would not already exist, and then merge again.

To do this:
  1. Click your name at the top.
  2. Select Setup.
  3. On the left side under App Setup, select Customize > Accounts *[Contacts] > Fields.
  4. Scroll down to the custom fields and select "Edit" next to the custom field.
  5. Change the internal name, or the API name, to something different.
  6. Save.
  7. Merge the duplicates again.