After finding that the gate at P4A-771 was still under fire, General Hammond orders the iris closed. This is not necessary as the wormholes are one-way and nothing could have come through the gate back at them. This may be protocol, given the receiving gate will chevron-lock the sending gate's symbols, and therefore could be used by hostiles to "return the call"
When the gate is fixed after the overload, the SGC redial P4A-771 to search for Jack and Sam, but on the Dialing Supercomputer, the chevrons dialed are those for Abydos [The first ever planet visited in the Stargate film - dialed with chevrons: Taurus, Serpens Caput, Capricorn, Monoceros, Sagittarius, Orion] and not that of P4A-771.
Sterno, while referenced several times, has not been used by the military for several decades; much less by tier one units (as any units in the SGC would be).
Col O'Neill something says to Capt Carter about being 1M LY from home. The 7 symbol Stargate addresses are all in the Milky Way galaxy, so the maximum distance from earth is on the order of 100K LY. Even if you include the LMC and SMC, satellite galaxies, it's under 200k LY.
General Hammond might be an Air Force general but that doesn't mean he can just order compliance with Teal'c and Daniel Jackson's (possible) request to go to Antarctica; he may not have the authority over the planes needed to do this. But no such actual order is shown; Daniel says nothing more than "General, Permission..." before General Hammond interrupts by saying: "Granted." Daniel might have been asking permission to ask someone else's permission to start the related process.
The SGC received SG-1's iris code prior to the sound of the gate activating, which would be impossible, since no transmissions could come through prior to the gate activating.
If you play the scene of the gate overload in slow motion, you can see the that the image of the clamp exploding is the same clamp just digitally flipped. You can tell because the same 2 triangle glyph can be seen in each scene. There is also one frame of the gate with the green screen and the platform that SG1 jumped off of.
During the opening sequence all of the tanks and other equipment in the facility have alien lettering/numbers or symbols. But on a big enough screen regular Earth number calibrations can be seen on the pressure gauge as the camera passes it.
No explanation is provided for why Carter wouldn't try another gate address first. Once she realized Earth's gate wasn't working there were other safe planets she could have tried gating to instead.