1) to output multiple selections from a multi select list, you need to use the php implode function. for example:
<?php echo((isset($_POST["Quote_Request_Project_Info_Project_Type"]))?implode(", ",$_POST["Quote_Request_Project_Info_Project_Type"]):"") ?>
2) There are some unneeded script tags, delete the following code:
var Quote_Request_group_Please_select_the_option_that_best_describes_your_project_Spry = new Spry.Widget.ValidationSelect("Quote_Request_group_Please_select_the_option_that_best_describes_your_project_Spry",{validateOn:["blur"]});
var Quote_Request_group_Do_you_require_scriptwriting__1_Spry = new Spry.Widget.ValidationRadio("Quote_Request_group_Do_you_require_scriptwriting__1_Spry",{validateOn:["blur"]});
var Quote_Request_group_Video_Delivery_Spry = new Spry.Widget.ValidationSelect("Quote_Request_group_Video_Delivery_Spry",{validateOn:["blur"]});
var Quote_Request_group_What_is_the_projected_length_completed_run_time_of_your_project_Spry = new Spry.Widget.ValidationSelect("Quote_Request_group_What_is_the_projected_length_completed_run_time_of_your_project_Spry",{validateOn:["blur"]});