Other mistake: During the fight with Suitor, Charlie drives his car into the building. When Ramsey's ship explodes, the explosion is strong enough to bring the building down, yet at the end, Charlie is driving that exact same car. That car should have been totaled in the fire alone.
Character mistake: When Shep and Charlie need to stop the aliens from tracing the power signal, he impatiently rips the driver's door off Charlie's Festiva because he was taking too long to unlock it. However, Shep gets into the car from the passenger side before Charlie has even retrieved his keys from the detached door. Why would Charlie leave the passenger door unlocked but make a point of locking the driver's door?