Medium Large Transport; Low Wing; 2 Turbojet Eng
Flight Crew Last 90 Days 177; Flight Crew Type 8944
Communication Breakdown; Confusion
ATC Issue All Types; Deviation - Speed All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Human Factors
As pilot monitoring; I checked in with SoCal after takeoff at 1;500 feet.  I normally prefer to postpone check-in until flaps are up; but this is a busy frequency and we were heavy so we had a bit of time before acceleration to clean up speed.  Departure's instructions to us were mumbled; but both the Captain and I understood him to say to turn left to 185 and 250 knots until PEVEE.  I read this back.  He responded with a similarly mumbled response which I understood to be clarification of the speed restriction until PEVEE; to which I responded 'Roger.'  By this time we had to change configuration to capture the heading; and call for and select flaps up concurrently with the communication.  Shortly thereafter; Departure queried our speed; I responded that we were accelerating to 250 knots (we were heavy; and the airplane was slow to accelerate).  A few moments later; the Controller queried our heading.  I responded; '185.'  He was upset and issued some instructions that were not completely intelligible; but seemed to indicate we were to proceed direct to PEVEE.  I responded with our understanding of our instructions; and he responded angrily with something along the lines of; 'Turn direct to PEVEE; maintain 250 knots; climb and maintain 13;000.' 'Why would you take a clearance you weren't sure of?'  I read back the clearance; but didn't answer his last question.
Pilot not flying reports of a mumbled transmission that he accepts and turns to what he thinks he heard; along with maintaining a speed he thought he heard to maintain.  Controller questions heading and speed and then comments to pilot asking why they would take a clearance they weren't sure of.