The National Labor Relations Board general counsel’s office signaled its intention to continue tightening the screws on labor unions in a trio of advisory memos.

The advice memos instructed regional board attorneys to find that unions violated federal labor law by displaying a balloon of a cat at a construction site and failing to properly track a member’s grievance. A third memo advised that a coal power company could stop deducting union dues from employees’ paychecks after their local affiliate merged with another union.

All three cases closed without a ruling from an administrative law judge or the board. Nonetheless,...