Since this is a plot point that has been constantly debated throughout the entire run of the Stargate franchise, here's something I would change:
Make the Stargate public knowledge from the very beginning, and actually allow the world to react to the news instead of keeping it a secret the whole time.
Thinking about the ramifications of that makes my head hurt. There are a ton of plots that Stargate couldn't do, from huge and dramatic (like whole nation states wanting to up and move to other worlds, and then getting into conflicts) to alien fast food franchise rights.
I forget the name of the two episodes with the Ashen (one was a year number), but those had a future where people were aware of the gate.