The jump into the pool would have either caused significant injuries or been fatal for both detectives. Hammer Bridge Drop/Buried Alive/Cola (2003) proved this when they dropped a dummy into water from a similar height than was depicted in the program. While the world record for high dives is over 170 feet, the people doing so have suffered injuries such as broken legs and a broken back.
Police do not wear guns in interrogation rooms.
Riggs states that when he was in SEAL training he did HALO jumps (i.e. High Altitude Low Opening military skydives) in which he opened the parachute just a couple hundred feet from the ground. However, even though the purpose of a HALO insertion is to avoid (radar) detection, the typical altitude when the jumper pulls their ripcords is around approx. 1000 to 2000 feet. Considering that jumpers are traveling at terminal velocity of 110 to 125+ miles an hour, and that a parachute usually is packed to take from 300 to 800 ft. to open, there is no way (especially in a training scenario) that a jumper would intentionally open that low to the ground.
During the program, we are shown two pages of Lieutenant Commander Chad Jackson's Official Biography in his Naval Special Warfare Command personnel folder. On the photo page, it is quite obvious that he is not wearing the appropriate insignia for a member of a Seal Team. He is not wearing the Seal Trident.
In the file for the SEAL, he is listed as being with SEAL Team Delta (phonetically the 4th team). SEAL team designators are numeric, not phonetic, so in this case he would have been with SEAL team 4.
In the end credits, Arnell Powell's character name is Dr. Nathan Cox, but his name tag says Logan Cox.
More than once the subtitles are wrong in stating who is talking, mixing Riggs and Murtaugh.
There was no reason to jump out the window, throwing the bomb out the window would have worked just fine. Shooting it was also pointless, the bomb had less than 5 seconds when he went out the window, it would have never made it to the ground before detonating. And shooting the bomb wouldn't detonate it.