Is there a means to set the owner of all objects in a PostgreSQL database at the same time?

You should only ever manipulate system catalogs directly, if you know exactly what you are doing. It may have unexpected side effects. Or you can corrupt the database (or the whole database cluster) beyond repair.

Jeremy's answer, while basically doing the trick, is not advisable for the general public. It unconditionally changes all functions in a schema. Are you sure there are no system functions affected or functions installed by an additional module?
It would also be pointless to change the owner of functions that already belong to the designated owner.

First, check if REASSIGN OWNED could work for you:

change the ownership of database objects owned by a database role

You have to list all roles to be disowned explicitly. But it also reassigns functions.

To assign all functions (and no other objects) in a given schema to a new owner (optionally regardless of previous owner):

SELECT string_agg('ALTER FUNCTION ' || oid::regprocedure || ' OWNER TO foo;', E'\n') AS ddl
FROM   pg_catalog.pg_proc p
JOIN   pg_catalog.pg_namespace n ON n.oid = p.pronamespace
WHERE  n.nspname = 'public';
-- AND p.relowner <> (SELECT oid FROM pg_roles WHERE rolname = 'foo')
-- AND p.proname ~~ 'f_%'

This generates the canonical SQL commands ALTER FUNCTION ... to change all functions (in the specified schema). You can inspect the commands before executing them - one by one or all at once:

ALTER FUNCTION public.bar(text, text) OWNER TO foo;
ALTER FUNCTION public.foo(x integer) OWNER TO foo;
...

I included some commented WHERE clauses you might want to use to filter the results.

The cast to regprocedure produces a valid function name with parameters, double-quoted where necessary, schema - qualified where necessary for the current search_path.

The aggregate function string_agg() requires PostgreSQL 9.0 or later. In older version substitute with array_agg() and array_to_string().

You could put all of this into a DO statement or a function like demonstrated in this related answer:

• Drop all functions in a namespace? (Execute generated DDL commands?)

In Postgres 9.5 or later, you can simplify the query using new object identifier types regnamespace and regrole:

SELECT string_agg('ALTER FUNCTION '|| oid::regprocedure || ' OWNER TO foo;', E'\n') AS ddl
FROM   pg_catalog.pg_proc
WHERE  pronamespace = 'public'::regnamespace;
-- AND relowner <> 'foo'::regrole
-- AND proname ~~ 'f_%'