Should a father prevent his 16-year-old son from working in a place that shows prohibited films, or is it sufficient for him to merely warn him, and will the father be held accountable before Allah if his son watches those forbidden acts?

A father is not obligated to prevent his son from undertaking a permissible job simply because there is a television displaying objectionable content. Rather, he should forbid his son from watching such content and advise the employers. If the son happens to see some objectionable things, there is no sin upon the father, Allah willing, because going to work is permissible, and these incidental matters are not intentional. If permissible intentions were to be forbidden because of such things, people would face extreme hardship.