Sheppard, Weir and Bates are discussing Teyla. After Bates is dismissed, Sheppard walks round the table and Bates' chair has disappeared. When Sheppard goes to walk around the table again' it has reappeared.
The guard that bars Teyla from seeing Dr. is Weir is wearing a South African flag patch. All of the colors on the patch are too bright compared to the actual colors of the SA flag, and his patch has from white borders on all sides. (Flag borders either have no extra color or are gold.)
This is incorrect. Flag patches (both in Stargate and in real life) have a stitched border ('merrow' or overlocking). On the USA and Czech flag patches, it is gold; on the Canadian, red; on the Scottish, Italian, Russian and UK, white; on the German and Australian, black; on the Croatian, blue... It's presumably a style style choice for each country. Concerning the South African flag, the thread colors of patches rarely match the Pantone specifications for the original flags precisely. Moreover, in universe, the uniforms and patches would have been manufactured in the USA.
During the scene when Teyla is dragging Lt. Ford through the Stargate, you can see her shadow before the steps through the event horizon.
Dr. McKay comments that the nearest burger joint is "300,000,000 light-years away". The Pegasus Dwarf Irregular Galaxy is actually only 3,000,000 light-years from the Milky-Way, it is one of several dwarf galaxies that orbit the Andromeda Galaxy. While most people might have said "300 million light-years" to be sarcastic, or because they don't know the actual distance, Dr. McKay prides himself on being one of the smartest people on the planet and always states accurate measurements, even when making a joke.