Show clients with staff assigned and no staff assigned
You are using deprecated syntax for joining tables that doesn't allow for OUTER joins. 

I'm not 100% sure what you're trying to accomplish because I can't see your data, but it seems to me like you're performing JOINS when you might want LEFT OUTER JOINS. 

First thing to do is to rewrite your query using JOIN keywords.

SELECT 
  g.name AS group,  
  cl.name_lastfirst_cs AS client
FROM 
  clients cl
JOIN
  link_group lg
ON
  cl.zzud_client = lg.zrud_client
JOIN
  groups g 
ON 
  lg.zrud_group = g.zzud_group
WHERE 
  lg.zrud_group = ? 
ORDER BY 
  cl.name_lastfirst_cs


Next, try using LEFT OUTER JOINs. 

SELECT 
  g.name AS group,  
  cl.name_lastfirst_cs AS client
FROM 
  clients cl
LEFT OUTER JOIN
  link_group lg
ON
  cl.zzud_client = lg.zrud_client
LEFT OUTER JOIN
  groups g 
ON 
  lg.zrud_group = g.zzud_group
WHERE 
  lg.zrud_group = ? 
ORDER BY 
  cl.name_lastfirst_cs


Here is a decent visual representation of the different kinds of JOINS using Venn diagrams: http://www.codinghorror.com/blog/2007/10/a-visual-explanation-of-sql-joins.html