In your subs with an error handler, you need the red exit sub before the error handler.
Without the exit sub, the code will ALWAYS fall thru to the error handler. That's why you were getting those pesky error messageboxes when there was no error.
Code:
Public Sub cmdOpenTable_Click()
On Error GoTo problem_Error
DoCmd.OpenTable "tblBIns"
DoCmd.SelectObject acTable, "tblBins"
DoCmd.Requery
Exit Sub
problem_Error:
Select Case Err
Case 7874
MsgBox " Create New Table! "
Case Else
MsgBox Err.Number & ":" & Err.Description
End Select
End Sub