Character mistake: John would have no reason to ask the CT technician if she had any results. He says "that was a long one," indicating he's had this done before and should know it typically takes around 24-48 hours to get results. (Likely just a line of dialogue added for the benefit of the audience, who may not know.)
Character mistake: [Story 1: Hungry Joe] It isn't clear what blood test results the doctor receives for Joe, but Laura pleads that she "really needs to know what's wrong with her son" because "He eats, he eats, and he eats, and he never stops." The doctor dismisses Laura's concern and replies, "Growing boys eat... we'll see you in six months." The doctor should order additional tests. Blood tests can show "false negatives" and the appropriate blood tests may not have been ordered in the first place. (00:04:25 - 00:05:18)
Character mistake: The Captain of the USS Fragasso comes onto the bridge. A Petty Officer says, "Officer on deck," and salutes while looking out the forward windscreen. He should have said, "Captain on the bridge" and not saluted.