Factual error: Looking at a nuclear explosion that close will burn your retinas irreparably. One can be blind 30 miles away, just by seeing the flash. The little girl at the start is looking directly at the explosion when it hits, and continues to watch.
Episode #1.6 - S1-E6
Continuity mistake: Sami takes Maya directly from the location where Tommy Dark's body is found to his home, but Maya's outfit is completely different when they arrive.
Second Date - S1-E2
Continuity mistake: At the deli, Jane orders plain bagels with cream cheese. When she gets home, she has everything bagels with lox.
Episode #1.1 - S1-E1
Continuity mistake: When Emma gets a pen out of her bag so that Dexter can write his number, the pen is upright. When the shot cuts, it is upside down, then it is upright again in the shot after that. (00:35:04)
Paul Is Dead - S1-E6
Factual error: The female British astronaut is in her space suit. There is a supposedly British flag on her left sleeve. But the flag is wrong. The red diagonal stripes are centered on the white field. They should be off-centered by 3/5 of the white space. Not centered. This is a common mistake you find in British flags bought outside the UK.
Continuity mistake: As Rick is getting informed about the CRM's future plans, he is holding his knife under the table. The next shot shows his hand on the table, before showing his hand holding the knife under the table again. (00:23:50)