This is the first time we hear of the Prime Directive
When Kirk goes to destroy Landru, Landru deactivates his phaser. Yet a few moments later, Kirk draws it to fire on a Lawgiver approaching him, despite already knowing it has been deactivated.
The U.S.S. Archon wasn't violating the Prime directive--the Prime Directive was formed in 2253.
You can briefly see a trail of burnt gunpowder leading up to one of the panels that exploded when the Landru computer blew up - the smudge disappears in subsequent shots
Kirk and Spock approach Landru's chamber via a long hallway leading straight up to the doors. But when they enter the chamber, the audience can see the open doors behind them and
there's a solid blue wall there instead of the long hallway.
When Kirk orders the landing party to fire their phasers on stun, McCoy fingers the phaser trigger but nothing comes out of his weapon.
As Festival begins, the landing party runs for cover. Watch and you can see a big thrown rock bounce off the head of one of the security guards. He doesn't even seem to notice.
Kirk and his team ignore the Prime Directive by beaming down in plain sight before they know anything about the planet or its inhabitants. In other episodes they always beam down secretly.