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Duplicate rules interfere with Process Builder, you will get a Process Builder error rather than an alert about Duplicates, so set it to Report rather than Alert if you are using Process Builder on that object. This will be better in #Summer18 though.
See also Making Sense of Duplicate Record Sets and Some notes about standard duplicate management.
Note: There is a new feature called Duplicate Jobs, which will check for duplicates already in your org, but it is only available if you have Performance or Ultimate edition of Salesforce and it doesn't work on Custom Objects.
Notes
Some notes and observations about standard Duplicate Management. The more I use it, the more I like it.
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- Create a Duplicate Rule to Match on Contacts using the Standard Lead Matching rule on the cross object. That way if you look at the Contact, it will show the Duplicate to the Lead. Nice.
- The rule does not seem to pick up a duplicate IF the Lead is Converted - this is nice. Although I can't see any docco about it, and I can't quite verify it on my data set yet, so stay tuned on this one, or mention in the comments if you can confirm or deny.
Chatter Does Not Merge!
- OMG how is this even possible. When you merge two records, only the Chatter posts from the Master record are kept. And you have to manually re-attach Attachments to the Master record.
Report vs Alert
- Apparently the Duplicate matching rule runs when you open the record, so it may show as a duplicate even though there is no record in the Duplicate Record Sets (not sure how this all works though yet).
- When you are bulk importing via the API turn on Report and turn off Alert, otherwise records won't be created
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- First Name + Last Name + Email
- Last Name + Email (depending on if you deal with Families that share email addresses - may not be useful).
- First Name + Last Name + Phone (or Mobile)
- First Name + Last Name + Street
- Account Name
- Account Name + Phone
- Account Name + Street + City
Create your own
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Duplicate Record Sets
You know that great feature in Classic named Merge Accounts where you could just pick any two or three Accounts with similar names and merge them. You know that great feature in Classic on the Contact Related List where you can mere Contacts? Both of these aren't in Lightning, so unless you are fortunate enough to use the Nonprofit Success Pack - NPSP and their excellent Contact Merge function, then you're out of luck, right? Well not quite... but it's not great.
Announced in #Winter18 is the ability to create your own Duplicate Record Sets and merge them yourself. It's not very intuitive and it's not very easy to do, but at least you can do it. But I think it might be quicker to switch back to Classic to do it anyway.
Here is the limited docco on the "feature" https://help.salesforce.com/articleView?id=duplicate_management_duplicate_record_sets.htm&type=5
You can't use this feature on Custom Objects.
Duplicate Reporting
When you set Report on Standard Salesforce Duplicate Rules, it's not clear at all what Report does.
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