Since you don't really need to loop through everything - just until you know that you want to show the message box, you can just exit the for loop after showing the message box:
Sub ReplaceRaterDemographicCodes()
...
For Each Cell In Range("H2:H" & Range("H" & Rows.Count).End(xlUp).Row).Select
If Not Cell.Value = 72 And Not Cell.Value = 73 And _
Not Cell.Value = 74 And Not Cell.Value = 75 And Not Cell.Value = 76 And _
Not Cell.Value = 77 And Not Cell.Value = 78 And Not Cell.Value = 79 And _
Not Cell.Value = "" Then
MsgBox ("There are uncommon demographics listed. Please modify as needed.")
Exit For
End If
Next Cell
End Sub
This way the message box is only shown once and only if it fits your criteria.