CO2 has a critical temperature of 31 degrees centigrade, IIRC, so it dissolves in oil as a gas and makes it more fluid, but it does not dissolve the oil into itself as a solvent because the oil is deep and at a higher temperature than the critical point.
N2 is not very soluble in oil. Flue gas is 80% N2 and 20% CO2, and since you have to compress it to pump it, the CO2 is going to condense anyway so you might as well dump the N2 to atmosphere after using the expansion for cooling.
CO2 liquid is going to dissolve things in your pipeline if you keep it as a supercritical fluid. It also forms hydrates and plugs things up if it gets cold. I don't know how they move it around without it crapping things up. Maybe they line the pipeline with plastic? Or insulate it and keep it hot? If any lurker out there knows, elucidate me.
We keep it dry and supercritical.
Now I have a question for you.  Won't the CO2 stay supercritical at well pressures even though the temp is high?  Or... I guess its only for wells where the pressure has depleted anyway, heh?
In thermo-speak, any temperature beyond 31°C is "supercritical" for CO2.  "Critical" is the point at which the distinction between the liquid and vapor phases disappears; hotter than that, you have one fluid phase regardless of the pressure.

Critical pressure for CO2 is 1072 psia.  As liquid CO2 is more dense than water at reasonable temperatures, it will tend to stay a dense fluid and develop considerable hydraulic head as you go down an injection well.