Factual error: There is not a snowball's chance of Howard becoming an astronaut. He suffers from cardiac arrhythmia, something about which he is completely open. "Transient" or not this is easily detectable by a simple electrocardiogram, which is a fundamental part of the many medical examinations a potential astronaut will have to pass. He wouldn't even be allowed to start basic training. Note also that during his basic training he shows signs of severe stress and trauma which would inevitably trigger a cardiac episode. Even if it didn't the fact that he was falling apart at the seams would have him removed from the programme for his own good.
Continuity mistake: After Howard and Bernadette are pronounced husband and wife, when they kiss the camera angle switches to an overhead shot, but as it zooms out (to a digital image) things change - such as the configuration of the rooftop, or things move - such as the cable dishes, or things even vanish - such as air-conditioning units.