To check on whether you need to refinish or just thoroughly clean older wood furniture, first try cleaning the piece a few times using a good furniture cleaner on a cotton cloth. Let it dry between tries. If the wood finish begins to clear, proceed with cleaning. If it remains dark, marred or alligatored, then refinish.
Whenever you are glueing glass you must consider the visibility of the adhesive. If the glass is translucent, you will want a glue that dries as clear as possible. Before glueing any glass bond be sure that the glass is clean, free of any oil (even from your fingers) and dry.