Armen,
First, I recently realized that I shouldn't have jumped on you about the term "super critical". On my Mollier diagram the dense phase region is labeled "SCF" for "Super Critical Fluid". It is just that the term "critical" (and by implication "super critical") is used so often in fluid mechanics for so many unrelated things that I start feeling that the use of the term should be discouraged. Just my own bias, sorry.
Also, all of my references have the critical point at 87.76F (360.9K) and 1070 psia (73.8 bara). You might want to check to verify the 304K you referenced.
For your first question, I think I have liquid CO2 anywhere less than the critical temperature at a pressure greater than the Boiling Line as long as temperature is greater than the Melting line.
Any time you are dealing with pressurized CO2 you should be concerned. A long-time poster on these boards named Montemayor once posted an example of a leak in a liquid CO2 vessel. Pressure dropped isothermally to the saturation line, then pressure and temperature followed the boiling line down to the sublimation line to atmospheric pressure at around -120F (-84C). Most piping has problems at those sorts of temperatures.
With CO2 Sequestration being such a hot topic this week, a lot of people are evaluating the pluses and minuses of gas transport vs. liquid transport and gas injection vs. liquid injection. The issues are complex and there is no one-size-fits all answer. You can compress dense-phase CO2, but it is one of the best surfactants on the planet--it will "clean up" all of the lubrication in a recip compressor and special materials are required. Starting with gaseous CO2 and liquefying it is very energy intensive (for a project I looked at last year, the total cost including capital and operating cost for this option was 3 times gaseous transport and twice dense phase transport).
Phase change happens with many fluid processes and it doesn't have to be a catastrophe, but unplanned phase change is rarely a good thing. For example, in your original example if your ending point had been a little bit lower pressure then the pressure traverse would have taken you from Dense Phase to Gas to Liquid--as a gas, a constant mass flow rate as required by the continuity equation would have yielded extremely high velocities that could easily be a noise problem or an erosion problem. If the CO2 should still be gas (or a liquid very close to saturation) at the pump suction then cavitation is a serious risk.
David