You're right, here is an updated version to do that:
Code:
Public Sub Remove_Spaces_in_All_Table_Data()
Dim tbl As DAO.TableDef,db as DAO.Database
dim fld as DAO.Field,sField as String
Set db=CurrentDb
For Each tbl In CurrentDb.TableDefs
If Len(tbl.Name) > 0 And Left(tbl.Name,4)<>"msys" Then
for each fld in tbl.fields
sField=fld.Name
db.Execute "UPDATE [" & tbl.Name & "] SET [" & sField & "] = replace([" & sField & "]," ","_")",dbFailOnError
'fld.name=replace(fld.name," ","_")
next fld
End If
Next tbl
Set tbl = Nothing
Set db=Nothing
End Sub