This blog post is all about explaining why flying (as a human) with Superman (being carried by him), is a not so great thing. This post is basically about trying to reason something logical with illogical assumptions, hence does not hold any real world value, but a lot of fun value.
1) Superman can fly and can attain super sonic speeds. There is something myseterious about his body and its perfectly aerodynamic - enough drag and lift to keep him in the sky(and hence does not retard his speed due to poor aerodynamics).
What are the problems:
1) Speed: Superman can attain supersonic speed. But there are problems that arise when he carries someone with him. Superman cannot attain Mach1 (1225 km/hour), because the Sonic Boom will cause temporary or permanent loss of hearing for the human with him (mostly because of the large problems associated with boom). Another assumption here: Sonic boom is usually associated with objects that are aerodynamic - and as said above, I assume Superman is aerodynamic. Another thing to consider with speed is the air friction. Althought I don't have statistics to quantify at what speed a normal human's dress would start burning, I can make a guess that air friction could burn out at high speeds. So, superman watch out when flying at high speeds along with a human. However, it is to be noted that superman is not subject to the air friction problem, because of some mysterious reason, his clothes never catch fire. :-)
2) Altitude/Height: Superman, as seen in TV, can even fly to space(where there is no oxygen) and come back with no issues. However, when he carries someone with him, he needs to ensure there is enough oxygen in air for the human. Anything above 18000 feet is death zone (roughly 5500 meters). There are other problems when superman flies with someone at higher altitudes. There should be significant radar signature for superman(with person). Hence, when superman enters a country's airspace, he could get picked up by defense systems. In the 1980s, a soviet airdefense personnel found radar blips, for which he did not inform his bosses about the blip and made a surmise that it cannot be US missiles, because he believed, if US had to attack, it would never attack with a few missiles, it would be a large fleet. It was eventually found that it was sunlight reflected from clouds (a false alarm). Read the story here. If Petrov had not been the air defense personnel in command and if Superman enters the air space of Soviets, he could even be one of the reasons for the cold war to have become a nuclear war.
What should superman do when a supersonic missile is fired at him? This is a tough question. Assuming that superman anyway cannot fly very high, he should make every effort to first reach the ground, drop the person and then go back to air and then fly hypersonic/ultrasonic/whatever and then destroy the missile, like he has been doing all throughout the superman story :-). The reason he has to fly back after dropping the person is that, if he doesn't, he would be hit by the missile. Being superhero, he does not suffer any damage :p, but the human will.. :).
In order to avoid the radar problem, superman has to fly at very low heights. In that case, he will have to be careful about the sudden change in topography, a gorge, a mountain etc. Also, there is this weird problem of having to be the target of some random AK47 or RPG when flying over Afghanistan. Hence, superman's flying with a person is not going to be that easy :).