I added a table and row counter, and that helped me obtain additional
information (related to the original error which prompted my error
handling). It still crashes in the error handler (5991: Can't access
individual rows in this collection because the table has vertically merged
cells), but I was able to use the table and row counters to look for the
offending row. There isn't any obvious merging, but there is a text form
field (regular text, unlimited length, bookmark area, fill-in enabled) in
table 2, row 1, column 1. As far as I can tell, nothing is protected.
Interestingly, that table shows onscreen as a 2x2 table so I wouldn't have
expected my code to even stop there, since I'm screening for rows with 4
columns.

My counters are not very elegant (I wasn't sure how to derive the row and
table number directly from atable and arow), but here is the current version
of the code.

Other than splitting cells, is there any type of "unmerge" command in Word?
I close the source documents without saving, so if the problem is merged
cells, perhaps there is a way to unmerge each table before processing, then
scan the table?

Thank you for any assistance or advice,
Keith

Sub CycleFiles()

Dim atable As Table
Dim arow As Row
Dim arange As Range
Dim TempDoc As Document
Dim RootDoc As Document
Dim NumTable as Integer
Dim NumRow as Integer

Set RootDoc = Word.ActiveDocument

PathToUse = "C:\KimTest\"

myfile = Dir$(PathToUse & "*.doc")

While myfile <> ""

   'Open document
   Set TempDoc = Documents.Open(PathToUse & myfile)

   On Error GoTo ErrorHandler

   NumTable = 1
   For Each atable In TempDoc.Tables
       NumRow = 1
       For Each arow In atable.Rows
           If arow.Cells.Count = 4 Then
               Set arange = arow.Cells(2).Range
               arange.End = arange.End - 1
               'MsgBox Len(arange)
               If UCase(arange.Text) = "V" Then
                   arow.Range.Copy  'the row will now be on the clipboard
                   RootDoc.Activate
                   RootDoc.Tables(1).Rows.Add
                   RDTRC = RootDoc.Tables(1).Rows.Count
                   RootDoc.Tables(1).Rows(RDTRC).Cells(2).Select
                   Selection.Paste
                   RootDoc.Tables(1).Rows(RDTRC).Cells(1).Range.Text =
myfile.Name
                   TempDoc.Activate
               End If
           End If
           NumRow = NumRow + 1
       Next arow
       NumTable = NumTable + 1
   Next atable

   'Close the modified document after saving changes
   TempDoc.Close (False)

   'Next file in folder
   myfile = Dir$()

Wend

ErrorHandler:
   Select Case Err.Number
       Case 5991    ' "Vertical Merged Cells" error.
           TempDoc.Activate
           TempDoc.Tables(NumTable).Rows(NumRow).Select
           'Selection.SetRange Start:=Selection.Rows(arow).Range.Start,
End:=Selection.End
           MsgBox "The macro has found a vertically merged cell." & _
                  "Please visually check the cell to ensure that " & _
                  "this is not a row with critical data. If it is, " & _
                  "open this source file manually, select the row, " & _
                  "unmerge it, then re-run this macro." & _
                  Chr(13) & Chr(13) & _
                  "This macro will continue to process the remaining
files", , "Error reading merged cells"
           On Error Resume Next
       Case Else
           ' do nothing for now?
   End Select
   Resume

End Sub