As the aircraft is a Cessna 310, a small, 6-seat airplane, it would not be carrying a "black box".
On the cockpit voice recording the pilot of the crashed plane reports that it had "three souls on board" even though four bodies were found in the wreckage. The crash investigator suggests that the pilot was not including himself in the count. However "souls" is a specific term used in the aviation and maritime industries to refer to the total number of people, both passengers and crew. An air crash investigator would have known this.
The aircraft involved, as seen in both the crash scenes and the three-view on the wall, is a 1960's era Cessna 310, a twin piston-engine low wing airplane that seats 6 total people. Cargo is kept behind the rear seats or possibly in small external wing lockers that would be far too small to contain an adult body. Therefore, Sherlock's remark that the murder victim was "inches below [the passengers'] feet" is not possible in this airplane.
The NTSB say they have found the black box - the Flight Data Recorder. The team then listen to the pilot talking to ground control and in the back ground the passengers raised voices. This data would be recorded on the Cockpit Voice Recorder, not the Flight Data Recorder/Black Box.
Wounds can be glued closed with cyanoacrylate glues (such as 'Krazy Glue') , not with 'model glue'. Models are not actually glued with glue but with a solvent that dissolves the plastic of both parts and then evaporates, causing a joint that is almost like a weld. It will only join plastics, not flesh or skin.
Much is made of the pilots having to make exact, precise weight calculations. The extra weight of the murder victim is mentioned as a major factor in the location of the crash site. Also, another pilot felt it was necessary to account for (and document) an extra 30kg for the cocaine on each flight. The extra weight for either of these scenarios would not make a noticeable effect on either outcome.
Sherlock immediately finds sand in the fuel tanks of the airplane. It is highly unlikely that the NTSB investigators would not have found this already, as fuel is one of the first things checked in an aircraft mishap.