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.
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 likely to be a name or other significant phrase. In this case, the Bynars probably meant for it to be easily guessed.