UPDATE statement with multiple joins in PostgreSQL

Your query should look like this:

UPDATE incode_warrants
SET warn_docket_no = incode_violations.viol_docket_no
FROM incode_violations
WHERE incode_violations.viol_citation_no = incode_warrants.warnv_citation_no
AND incode_violations.viol_viol_no = incode_warrants.warnv_viol_no;

You don't need any other join. With this query you just update a column in one table with values from a column from another table. Of course, it updates only when WHERE condition is true.

The same as valid UPDATE statement in Postgres:

UPDATE incode_warrants iw
SET    warn_docket_no = iv.viol_docket_no
FROM   incode_warrantvs  iwvs
JOIN   incode_violations iv ON iv.viol_citation_no = iwvs.warnv_citation_no
                           AND iv.viol_viol_no = iwvs.warnv_viol_no
WHERE  iw.warn_rid = iwvs.warnv_rid;
-- AND iw.warn_docket_no IS DISTINCT FROM iv.viol_docket_no -- see below

You cannot just use a table alias in the FROM clause as target table in the UPDATE clause. The (one!) table to be updated comes right after UPDATE keyword (if we ignore a possible ONLY keyword in between). You can add an alias there if you want. That's the immediate cause of your error message, but there's more.

The column to be updated is always from the one table to be updated and cannot be table-qualified.

You don't need to repeat the target table in the FROM clause - except for special cases like this:

• PostgreSQL: update with left outer self join ignored

This optional addition can avoid pointless cost by suppressing updates that do not change anything:

AND iw.warn_docket_no IS DISTINCT FROM iv.viol_docket_no

See:

• How do I (or can I) SELECT DISTINCT on multiple columns?

More in the excellent manual on UPDATE.

Your update a table, not the join

update incode_warrants ALIAS
set warn_docket_no = iv.viol_docket_no
from incode_warrantvs as iw 
...

UPDATE incode_warrants iw
     SET warn_docket_no = iv.viol_docket_no
FROM incode_warrantvs AS iwvs, incode_violations AS iv 
WHERE iv.viol_citation_no = iwvs.warnv_citation_no AND
      iv.viol_viol_no = iwvs.warnv_viol_no AND
      iw.warn_rid = iwvs.warnv_rid;