Plot hole: "Sight Unseen": Wells has the key to Lori's shackles. Weston, who knows this, knocks Wells out, but instead of taking his keys, uses a completely unnecessary (and considerably more difficult) set of bolt cutters to break the leg cuffs. (00:32:30)
Character mistake: The Eagle Koenig flies is called Eagle One. However, the number on the door behind him is plainly a four, meaning Eagle Four.
Suggested correction: This happens a lot. The number on the door is not the number of the Eagle, it's the number of the command module. The super structure and drive systems are Eagle One. Even then, there has been several Eagle Ones destroyed or lost. Eagle One is assigned its designation by the head of Recon, Alan Carter.
An Insidious Trap! The Flying Fleet - S1-E3
Revealing mistake: When Hayato attacks Bullface with the Liger missiles, the explosion does not follow at all the outline of the ground, it just cuts away in a straight line superimposed in the wrong spot. (00:18:15)
Witchcraft! - S1-E5
Visible crew/equipment: When Jonathan shuts the stable door the camera lights are reflected on it.