What are all of the requirements for a field to be set as the Key field?

Basically any data entry field can be a key field. It may not be a formula field.

I doubt a list user or Multi Select  field can be a Key field.

Did you have a particular field type which you wanted to be a Key field but was not able to be selected as such?

What I was trying to do was make the reference field for a child table be equal to a concatenated formula field and then match it to a concatenated formula field in the parent table which would be set as the key field.  And both of the formula concatenated fields are based on lookups/reference fields.  But, unfortunately, QuickBase doesn't tolerate any part of that idea.  Which I find disappointing since all the fields involved in this scenario are 100% unique (unique records that is).

Well, the key field of a Parent table may not be a formula.  There is no problem to have the Child table's reference field be a formula.

 One work around can be to have a form rule which takes the calculated value of what you want the Key field to be and save it in the key field.

The form rule would look like this:

When the record is saved
change the value of the field [My key Field] to the value in the field [calculated concatenated Key field]

Yeah ok.  I'm going to give that a try.  My first thought was to do something kind of similar using a URL button on the form, but a form rule would be easier. Thanks