Continuity: Just after the ship is first attacked, Scotty tells McCoy, "We can't fire full phasers with our screens up." Say what? The Enterprise couldn't operate transporters with the shields up, but it fired its phasers, full or otherwise, with the screens up every time it went into battle, and always had. If they'd been forced to shut their shields down every time they fired, the Enterprise would have been history long before this.

Factual error: How do the Eminiarians fire a weapon based on sound ("Decibels - 18 to the 12th power") up into the vacuum of space at the Enterprise?