I've created a test site with the petitions profile, here are the errors when creating a petition:
after step one:

Deprecated function: Function MongoCollection::setSlaveOkay() is deprecated in wh_petitions_create_petition_step_1_submit() (line 332 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Deprecated function: Function MongoCollection::setSlaveOkay() is deprecated in wh_petitions_create_petition_step_2() (line 404 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).

after step three:

Deprecated function: Function MongoCollection::setSlaveOkay() is deprecated in wh_petitions_create_petition_step_3_submit() (line 634 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Deprecated function: Function MongoCollection::setSlaveOkay() is deprecated in wh_petitions_create_petition_step_4() (line 666 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).

and after publishing the petition:

Deprecated function: Function MongoCollection::setSlaveOkay() is deprecated in wh_petitions_create_petition_step_4_submit() (line 778 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Undefined property: stdClass::$data in wh_petition_tool_shortenurl() (line 229 of /var/www/profiles/petitions/modules/custom/wh_petition_tool/wh_petition_tool.module).
Notice: Undefined index: max_bid in govdelivery_queue_set() (line 434 of /var/www/profiles/petitions/modules/contrib/govdelivery/govdelivery.module).
Notice: Undefined index: main in wh_petitions_create_petition_step_4_submit() (line 831 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Trying to get property of non-object in wh_petitions_create_petition_step_4_submit() (line 831 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Undefined index: main in wh_petitions_create_petition_step_4_submit() (line 832 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Trying to get property of non-object in wh_petitions_create_petition_step_4_submit() (line 832 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Undefined index: main in wh_petitions_create_petition_step_4_submit() (line 833 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Trying to get property of non-object in wh_petitions_create_petition_step_4_submit() (line 833 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Undefined index: main in wh_petitions_create_petition_step_4_submit() (line 834 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Trying to get property of non-object in wh_petitions_create_petition_step_4_submit() (line 834 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Undefined index: main in wh_petitions_create_petition_step_4_submit() (line 835 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Trying to get property of non-object in wh_petitions_create_petition_step_4_submit() (line 835 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Undefined index: main in wh_petitions_create_petition_step_4_submit() (line 837 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Trying to get property of non-object in wh_petitions_create_petition_step_4_submit() (line 837 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Undefined index: max_bid in govdelivery_queue_set() (line 434 of /var/www/profiles/petitions/modules/contrib/govdelivery/govdelivery.module).
Deprecated function: Function MongoCollection::setSlaveOkay() is deprecated in wh_petitions_create_petition_thank_you() (line 895 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).
Notice: Use of undefined constant warning - assumed 'warning' in wh_petitions_create_petition_thank_you() (line 910 of /var/www/profiles/petitions/modules/custom/wh_petitions/wh_petitions.form.inc).