How can I tell what is in a Postgresql tablespace?

In PostgreSQL, a tablespace can be used by any PostgreSQL database. (As long as the requesting user has sufficient privileges, that is.) I think this query

SELECT spcname, spclocation FROM pg_tablespace;

will show you the directory that index_old is using in the filesystem in PostgreSQL version through 9.1. Prowl around in there to see if something real is in your way. I'd be really cautious about trying to delete anything in there apart from using PostgreSQL's interface, though.

In 9.2+, try

select spcname, pg_tablespace_location(oid) from pg_tablespace;

Check pg_class to see what is located where:

SELECT 
  c.relname, 
  t.spcname 
FROM 
  pg_class c 
    JOIN pg_tablespace t ON c.reltablespace = t.oid 
WHERE 
  t.spcname = 'indexes_old';