Joe Flanigan does actually know how to fly the helicopter that Sheppard and O'Neill were in, but, for both budgetary reasons and safety concerns, Flanigan's shots inside the helicopter were all done in a studio or on location, and he was not permitted to try to fly.
The character of Simon Wallis (Dr. Weir's partner back on earth) features in Season 1's Rising (2004) and Home (2004) and Season 2's The Intruder (2005). Wallis is played by Garwin Sanford who also played one of the main Tollan characters, Narim, in Stargate SG-1 (1997).
The stairs in the control room have a message written in the Ancient language. It reads as following from top to bottom - "We hold these as the truth: A hearty welcome to those of other worlds visiting our home for the first time. Welcome again to those returning. You have been gone too long and your absence has weighed heavily on our souls. We are whole again that you are among us and we celebrate you being here again. As we leave for distant worlds we pledge to respect the lands of our neighbors and to act with integrity as ambassadors in peace time of our people. Travelers with open hearts will always be welcome. Refugees from tyranny may seek shelter under our roof and our people will lay down their lives to protect the weak and the just. Let this be our pledge to those inhabitants of this world. And all we may ever know we will always strive to come in peace as we go in peace and you will be welcome on our shores forever more."
While in the "dining room" of the female Wraith (Andee Frizzell), clearly seen on the table is the head of a creature. This creature is a Mastadge, which was seen in the original Stargate (1994) movie.
When Rising (2004) was filmed, there were four regular characters in Stargate SG-1 (1997), but only two of them (Jack O'Neill and Daniel Jackson) appear in the pilot. According to Amanda Tapping, who played Samantha Carter, her character and Teal'c weren't allowed to appear due to rights issues. They were created for Stargate: SG-1, and including them in the new show would mean using the work from one of the producers to boost a new, different show. Jack and Daniel already appeared in Stargate (1994) and therefore they weren't affected. Eventually, all four would appear in multiple Stargate: Atlantis episodes throughout its five seasons.