At the very beginning of SG1, the Goa'uld invade Earth, and then return somehow. How did they manage to return? There was no DHD, and somehow they didn't let it be known where they were going, IE, there was no log of the return. This seems a bit odd to me...
That's an excellent question, which was answered in the recently-released re-cut 'Children of the Gods'.
As noted on the Stargate Wiki:
When Apophis and his Jaffa infiltrate Stargate Command, they are able to leave without any apparent way of dialing or powering the gate. His Jaffa dialed out manually. In the "Final Cut" version, Apophis can be heard ordering a manual dial. This leaves the issue of where it got the power, though it should be noted that the gate was still hooked up.
Short answer - It's a mistake by the writer
In the commentary for the "final cut" version, Brad Wright and Richard Dean Anderson specifically mention that in the original script Jonathan Glassner (co-creator of Stargate) wrote the scene in such a way that it broke one of the fundamental rules of the Stargate universe, i.e that gate travel is uni-directional. The implication is clearly that Apophis dialled in, then left via another dialled in wormhole.
Brad Wright: The reason we had to put that other shot in, was because the way Jonathan originally wrote this opening scene, was uh, broke the rules of Stargate…
BW: …so that little moment where…
RDA: Which were?
BW: ...well, you can't go through a puddle and then step back through it. They had to stop and redial somehow.
RDA: Oh! That's true.
Apohphis then tilts his head at the gate and tells his Jaffa "K'on! A'nsi" in Goa'uld. Although there's no literal translation offered in either the episode or the script, I think we can reasonably assume that this is something along the lines of "take up defensive positions"
At around 4:40 (some 20 seconds of realtime later but an undefined amount of film time later), we rejoin the action in the gateroom where we see that another wormhole has been connected.
In the "Final Cut" version, the episode order is clearer. After the firefight, Apophis turns to his Jaffa and orders them to "Kala Chappa-ai" ("dial the gate")
Although it's not made clear how they do it, there's a couple of possibilities;
- Teal'c could have used the same device that was later retconned into the film continuum which basically attached directly to the gate and allowed a manual dial, described as a portable DHD
- The Jaffa had a power source powerful enough to power the gate, perhaps by using Liquid naquadah (e.g. from a staff weapon) or simply by diverting one of the electrical conduits on the wall and then moving the bezel around manually like Teal'c did in "Prisoners"