Here are my results when running test_slony_state-dbi.pl from a remote
Linux machine:

peter at peter-development-machine:~/slony1-2.0.2/tools>
./test_slony_state-dbi.pl --user=postgres --password=my_password
--host=10.0.0.80 --database=lustre --cluster=lustre_cluster

DSN: dbi:Pg:dbname=lustre;host=10.0.0.80;user=postgres;password=my_password;
===========================
Rummage for DSNs
=============================
Query:

   select p.pa_server, p.pa_conninfo
   from "_lustre_cluster".sl_path p
--   where exists (select * from "_lustre_cluster".sl_subscribe s where
--                          (s.sub_provider = p.pa_server or
s.sub_receiver = p.pa_server) and
--                          sub_active = 't')
   group by pa_server, pa_conninfo;


Tests for node 1 - DSN = dbi:Pg:dbname=lustre host=127.0.0.1
user=postgres password=my_password
========================================
pg_listener info:
Pages: 0
Tuples: 0

Size Tests
================================================
       sl_log_1         0  0.000000
       sl_log_2         0  0.000000
      sl_seqlog         0  0.000000

Listen Path Analysis
===================================================
No problems found with sl_listen

--------------------------------------------------------------------------------
Summary of event info
 Origin  Min SYNC  Max SYNC Min SYNC Age Max SYNC Age
================================================================================
      1     28741     29914     00:00:00     02:58:00    0
      2        18        18 1 day 01:24:00 1 day 01:24:00    1
      3        26        26 1 day 01:19:00 1 day 01:19:00    1


---------------------------------------------------------------------------------
Summary of sl_confirm aging
   Origin   Receiver   Min SYNC   Max SYNC  Age of latest SYNC  Age of
eldest SYNC
=================================================================================
        1          2      28741      28741      03:03:00      03:03:00    1
        1          3      29800      29913      00:00:00      00:18:00    0
        2          1         18         18  1 day 01:19:00  1 day 01:19:00    1
        2          3         18         18  1 day 01:19:00  1 day 01:19:00    1
        3          1         26         26  1 day 01:19:00  1 day 01:19:00    1
        3          2         26         26  1 day 01:24:00  1 day 01:24:00    1


------------------------------------------------------------------------------

Listing of old open connections on node 1
       Database             PID            User    Query Age
     Query
================================================================================


Tests for node 3 - DSN = dbi:Pg:dbname=lustre_slave host=10.0.0.82
user=postgres password=my_password
========================================
DBI connect('dbname=lustre_slave host=10.0.0.82 user=postgres
password=my_password','',...) failed: FATAL:  database "lustre_slave"
does not exist at ./test_slony_state-dbi.pl line 79

Tests for node 2 - DSN = dbi:Pg:dbname=lustre_slave host=10.0.0.81
user=postgres password=my_password
========================================
DBI connect('dbname=lustre_slave host=10.0.0.81 user=postgres
password=my_password','',...) failed: FATAL:  database "lustre_slave"
does not exist at ./test_slony_state-dbi.pl line 79
sh: - : invalid option
Usage:	sh [GNU long option] [option] ...
	sh [GNU long option] [option] script-file ...
GNU long options:
	--debug
	--debugger
	--dump-po-strings
	--dump-strings
	--help
	--init-file
	--login
	--noediting
	--noprofile
	--norc
	--posix
	--protected
	--rcfile
	--restricted
	--verbose
	--version
	--wordexp
Shell options:
	-irsD or -c command or -O shopt_option		(invocation only)
	-abefhkmnptuvxBCHP or -o option


I have no idea why test_slony_state-dbi.pl cannot connect to the two
slave nodes's DBs - the databases are plainly present on the nodes - I
can connect directly to them from the machine that I'm running the
test on, and see everything is in order.

Why might this problem occur?

Thanks,
Peter Geoghegan