WordPress Default Category and Custom Taxonomy Selected Attribute not Working After Searched in wp_dropdown_categories Array

Firstly, you have the same 'selected' parameter for all dropdowns. Secondly, get_queried_object() returns different objects in different template files. See User Contributions under get_queried_object() description in the Code Reference.

I’ve followed the link you’ve provided, so I suggest to use get_query_var(). It’s not enough information in the question to suggest something else.

<?php

/* Category dropdown */
$category_args = array(
    'selected' => get_query_var('cat'),
    /* Remaining parameters here */
)
wp_dropdown_categories( $category_args );


/* Location dropdown */
$location_args = array(
    'selected' => get_query_var('location'),
    /* Remaining parameters here */
)
wp_dropdown_categories( $location_args );


/* Job Type dropdown */
$job_type_args = array(
    'selected' => get_query_var('job_type'),
    /* Remaining parameters here */
)
wp_dropdown_categories( $job_type_args );

Also:

• Check all wp_dropdown_categories() arguments as you have a mess there.
• I’ve added the search values directly to URL and I see wrong search results as the taxonomies are nested in a weird way.