How can I find lines with very wide spaces in a Word document in VBA?

You need to look not for spaces (they are the most common), but for the reason for this behavior of the string. In particular, in this case, the stretching of the line seems to occur because the line ends with a line feed character (indicated by the number 2 in the figure) instead of a paragraph end character (indicated by the number 1). The line itself with such a stretch is marked with an arrow.

To see the difference visually, enable the display mode for non-printable characters. the icon.

If you want to search for these characters programmatically, via VBA, then the newline character has the notation vbLf, and the paragraph character vbCrLf

' Поиск строк с низкой заполненностью
Sub CheckLowFillLines()
  Dim Doc As Document
  Set Doc = ActiveDocument
  Dim WordApp As Application
  Set WordApp = Application

  LowFillThreshold = 61

  Dim R1 As Range
  Set R1 = Doc.GoTo(wdGoToLine, wdGoToFirst)
  R1.Select
  WordApp.Selection.Expand wdLine

  Do While WordApp.Selection.MoveDown(wdLine, 1) = 1
    WordApp.Selection.Expand wdLine
    If R1.Start = WordApp.Selection.Range.Start And R1.End = WordApp.Selection.Range.End Then
      Exit Do
    End If
    Set R1 = WordApp.Selection.Range

    If WordApp.Selection.Tables.Count <> 0 Then
      WordApp.Selection.Tables(1).Select
      WordApp.Selection.Collapse (0)
    Else
      If WordApp.Selection.Characters.Last <> Chr(13) And WordApp.Selection.Characters.Count < LowFillThreshold Then
        If WordApp.Selection.Paragraphs.Alignment = 3 Then ' wdAlignParagraphJustify
          LineNumber = WordApp.Selection.Information(10) 'wdFirstCharacterLineNumber)
          PageNumber = WordApp.Selection.Information(1) ' wdActiveEndPageNumber
          StdErr.WriteLine "Low fill factor in line = " & LineNumber & " on page = " & PageNumber
          FileName = ErrorFileNamePrefix & "Малое заполнение строки на странице " & PageNumber & ", строка " & LineNumber & ".pdf"
          WordApp.Selection.Range.HighlightColorIndex = wdYellow
          Call ExportPageAsPdf(Doc, FileName)
          Doc.Undo
        End If
      End If
    End If
  Loop
End Sub