The amount of blood on McKay's head wound changes from shot to shot.
Zelenka says 1200 feet is "almost the maximum depth of a nuclear powered submarine". Even many Cold War era submarines had operational depths of over 1500 feet and crush depths of 2400-3000 feet.
Griffin says Mexico was conquered in 1519. However, the Aztecs were defeated by the Spanish two years later, in 1521.
If the jumper is taking water at so great a depth, it shouldn't be trickling in, it should be coming in like a bullet.
Barring some special Atlantean technology, which is never mentioned throughout the series, regular two-way radio does not work under water. Communication would only be possible through either sonar-based technologies or VLF/ELF radio, which can only transmit a few characters per minute due to the low bandwidth that goes with the extremely low frequencies.
Increasing the atmospheric pressure inside the cabin of the jumper would work to help keep the water out and it would not cause the air in the cabin to escape faster. The increased air pressure would exert a downward force on the water making it harder to fill the empty space. It is the exact same principle as the diving bell, the bottom of a diving bell is able to be open because the pressurized atmosphere inside the bell is preventing the water from filling the empty space inside the bell.
McKay's display tells us that he has oxygen for a bit over two hours (after heating turning on the heater). Sheppard tells us that it takes several hours to prepare his jumper for the rescue mission. Even if McKay would not talk and scream that much, his oxygen would be fully consumed before Sheppard and Zelenka would be at his site to rescue him.
Captain Griffin claims that Columbus proved that the Earth was round. However, at the time of Columbus, the Earth being round had been widely known and accepted for over two thousand years. (Most flat earth beliefs stem from the 19th century.) Columbus was actually wrong in his theory since he predicted that he could journey directly to Asia by sailing West.