As pointed out at the end of the episode, the Bynar could have just asked for Starfleet's help! Somewhat justified, as their binary thinking meant they only saw two options and they simply couldn't take "No" for an answer.
Two humans are needed to operate the system to reboot the Bynar planet, yet they only kidnap one, Riker, and Picard only ends up on board by accident.
Forgot About His Powers: As the Enterprise is exiting spacedock, Worf and Yar ask where the transporter room is, causing the starbase commander to state that there's no time as the ship is almost clear of the station. Apparently their transporters can't do site-to-site transport the way a starship's can. Also, this is a massive starbase designed for servicing starships, and is several miles tall, but apparently it does not have tractor beams.
Not So Different: Bynars take children and remove part of their brain, replacing it with cybernetic implants that mean they are forced to work in tandem with another Bynar. In retrospect, what exactly makes them any better than the Borg?
They only do it to themselves?
Fridge Brilliance: This way of life actually has its perks. For example, former Borg drones like Seven-of-Nine and Icheb are Omnidisciplinary Scientists even after they are severed from the Collective. This gives the kind of Broken Aesop that being raised the Borg way is actually beneficial, so long as you provide the right socialization to drones once they are released from the hive mind as adults. To the Bynars, what they are doing is ensuring that every child of their species has the same intellectual advantages.
The Password Is Always Swordfish: The code to begin transferring data from the Enterprise computers to the Bynar master computer (and unlock normal functions) is a short sequence in binary that Picard and Riker figure out quite quickly. Data says it's like to be a name or other significant phrase. In this case, the Bynars probably meant for it to be easily guessed.