The syntax error is due to insufficient quotes. You have use two single quotes to get one when using them inside OPENQUERY
ie
SELECT *
FROM OPENQUERY (LS_RDB_DWH, 'SELECT * FROM RDB_DWH.ENTITY_DIMENSION WHERE PD_RDB_ENTRY_DATE = ''2012-10-31 03:10:37.0053840''')
Far away is close at hand in the images of elsewhere.
Anon.