In all the medium and long shots in his cell, G'Kar is writing right-handed. In the close-up after Garibaldi leaves the cell he is writing left-handed.
When the Whitestar enters Jupiter's atmosphere, Lennier reports that the external pressure is at "...two standard gravities." Pressure in this case would be expressed in standard atmospheres, not gravities.
When the shadow ship fires its beam weapon, Sheridan says that it ignites Jupiter's hydrogen, which is impossible. To do that, there would have to be oxygen available to allow a burn effect. Jupiter's atmosphere is composed of 90% hydrogen, 10% helium, and traces of methane, but no oxygen. The same consideration applies when Lennier suggests that the effects of opening a jump point in the hydrogen-rich atmosphere would be "...explosive, at best."