track her down? the set of a film?

"A couple of weeks ago I brought a date here. He chats her up. Middle of the week he tracks her down on the set of a film she's working on, flatters her with a load of poppycock, then asks her out."

Does "middle of the week" mean "one day of that week after I brought a date here"?
What does "tracks her down on the set of a film" mean? What did he do anyway?

"Middle of the week" means around Wednesday. "Track her down on the set of a film" means to search for her and then find her at the site where a movie is being filmed.