Is it a flight violation to mishear ATC instructions for exiting the runway? I was on landing rollout and misheard a tower "turn off at xxx switch ground" call. We read back the incorrect taxi way and turned off there and switched to the ground frequency. After our incorrect read back we were not contacted again until ground told us to call tower. I was under the impression that the landing aircraft had the right of way over any traffic behind them, even on roll out. I was also under the impression that a tower cannot stop you from using the whole runway.

Is missing a directed turn off a runway a flight violation? If so what FAR/AIM or regulation did it violate? Is the fault with us for mishearing or with the controller for not correcting us? Does this count as a runway incursion? Does the controller maintain responsibility for maintaining separation until we taxi clear?

To answer a few of the questions from below:
when we contacted the ground controller, they gave us a phone number to contact tower then gave us a taxi clearance. When they told us to call i became concerned with receiving a flight violation. We were not corrected to my knowledge, we only heard radio traffic once we had turned off the runway. This was also not a LAHS operation.  

another question: From the AIM 4-3-20 it says : "the following procedures must be followed..." "exit the runway without delay" 
" is that at the discretion of the pilot? 

also if tower gives you a taxiway instruction to leave the runway is that an instruction or a clearance?  

Is it a good idea to call the local FAA office and see if they have opened an investigation?
I don't think you violated any regulations. It was an ATC instruction, not an ATC clearance. 

It was an instruction you were unable to comply with. The instruction was badly timed and was obviously not clear since you did not correctly understand it.  In the busy time during the landing roll, you understood something different, and read back what you understood it to be. 

The landing roll-out can be a busy time needing the attention of both pilots.  ATC issuing an instruction while you are basically still in the landing roll should not be expected to be complied with unless it is happens to be convenient for you to do so.   

Many airlines SOP say that you do nothing until you are clear of the runway. Both pilots remain heads up and don't touch anything. The pilot in command alone will decide where it is safe to tun off the runway. If ATC makes a "Request", and it can be safely complied with, then the PIC may decide to deviate from SOP and comply. 

If you ran off the side of the runway trying to comply with an ATC "request", who do you think will be held responsible? (I'll give you a hint, it won't be ATC)

This is a prime example of why ATC should not be doing this.