I would suggest you break this up into smaller pieces and then begin to put the joins together.
At the core of everything that you want is the latest contact_date/status/note for each client. You can get each of those using aggregation:
SELECT client, MAX(contact_date) AS latestContact
FROM client_contact_date
GROUP BY client;
SELECT client, MAX(mod_time) AS latestNote
FROM client_notes
GROUP BY client;
SELECT client, MAX(mod_time) AS latestStatus
FROM client_status
GROUP BY client;
The first query can easily be outer joined to the client table to get the client information since there should only be one row for each client. For the last two of those subqueries, you'll have to join back to the original tables (notes, status) to get the information like this, because the row must be matched by time as well:
SELECT n.client, n.client_note, n.mod_time
FROM client_notes n
JOIN(
SELECT client, MAX(mod_time) AS latestNote
FROM client_notes
GROUP BY client) t ON t.client = n.client AND t.latestNote = n.mod_time;
SELECT s.client, s.client_status, s.mod_time
FROM client_status s
JOIN(
SELECT client, MAX(mod_time) AS latestStatus
FROM client_status
GROUP BY client) t ON t.client = s.client AND t.latestStatus = s.mod_time;
Once you have all of those things, you can use outer joins to bring the latest rows of information together:
SELECT c.id, c.clientName, c.operators, cd.latestContact, cn.client_note, cn.latestNote, cs.client_status, cs.latestStatus
FROM clienti c
LEFT JOIN(
SELECT client, MAX(contact_date) AS latestContact
FROM client_contact_date
GROUP BY client) cd ON cd.client = c.id
LEFT JOIN(
SELECT n.client, n.client_note, n.mod_time AS latestNote
FROM client_notes n
JOIN(
SELECT client, MAX(mod_time) AS latestNote
FROM client_notes
GROUP BY client) t ON t.client = n.client AND t.latestNote = n.mod_time) cn ON cn.client = c.id
LEFT JOIN(
SELECT s.client, s.client_status, s.mod_time AS latestStatus
FROM client_status s
JOIN(
SELECT client, MAX(mod_time) AS latestStatus
FROM client_status
GROUP BY client) t ON t.client = s.client AND t.latestStatus = s.mod_time) cs ON cs.client = c.id;
I would like to make one comment though. I see that you are storing operators as a list. This breaks normalization, and is generally a very bad idea. For me information, see Is storing a delimited list in a database column really that bad?
Here is an SQL Fiddle example with my query.