When Deb passes by the playpen, she is wearing her standard boots. The camera cuts to Dexter for his line, "How was your nap?" When the shot returns to the couch, Deb sits on the toy keyboard, and she is barefoot approaching the couch and sitting on her leg and for the remainder of this scene.
There are many issues with Lumen's driver's license: On Lumen's driver's license her height is 5'3"; Julia Stiles is 5'8. Her driver's license is shown as being Class C, and the report below that says it's Class A; the regular non-commercial driver's license in Minnesota is Class D. Finally, the reason Dexter finds Lumen's driver's license to begin with is by running her fingerprints; Minnesota does not require fingerprint registration for a driver's license.
When Dexter cross-checks Lumen's fingerprints on his computer, it displays both an actual drivers license with picture and a transcription below. The expiration date of each are different. Also, neither lists a date of birth.
At the end when Dexter is showing Lumen the barrels with bodies in them at Boyd's secluded swamp dump site, there is a vehicle in the near distance with its lights on.
The authorities do not let witnesses around town when they have placed them in safe houses for protection. That would cause the safe house to no longer be safe and the witnesses to not be protected any more.
There is no reason for La Guerta to prevent testing Quinn's hypothesis that "Kyle Butler" is Dexter by having the FBI show Trinity's family a picture of Dexter. To the contrary: she has nothing to lose but a lot to gain.