The carrier they land on is the USS Bennington (CV-20). On 15 January 1970, Bennington was placed out of commission. Making it impossible for the flying sub to have landed on that carrier.
During the underwater recovery of the space capsule at 240 feet, Crane and two crew members in scuba gear, use underwater blow torches to rid the capsule of the alien growth. In upward camera angles, exhaust bubbles from the scuba gear can be seen striking the surface of the water directly above the divers and moving out horizontally. Clearly indicating the surface of the pool where this scene was shot and not representative of the capsule recovery at 240 feet.
As the flying sub departs with the probe, the Seaview is plainly surfaced already. Then Chip says to surface and you see the sub at depth.
After the Admiral shoots through the door vents, the next shot is of the monster outside the door. In the upper right side, you can clearly see a man wearing a beige cap behind the monster and smoking a pipe while reaching behind the monster.
When the Admiral brings the probe aboard he his worried about contamination but then unprotected crewman handle it before the decontamination crew gets to work.
This episode features several Thompson sub-machine guns, most likely the M1928A1 model common during World War II. The selective fire (or fully automatic) Thompson fires from an open bolt, meaning the knob on top of the weapon must be in the rear position in order to fire. On several occasions (at 36:00 in the missile room for example), both Nelson and Crane are carrying their Thompsons with the bolt set forward. These weapons are therefore not ready to fire.