I rarely clean the old oil from my slow-cooker, is it OK? I put some chicken/beef into my slow-cooker, pour some olive oil and cook it for 4-5 hours. After that, if some meat is still left in the cooker, I may heat it up again the next day or the day after the next day, etc. 
Then, when all meat is finished, I just throw away the oil &amp; meat juices from the cooker but don't wash the cooker with water. I put new raw meat, pour some fresh olive oil and repeat again the cooking process. Is it bad that some residues of the old olive oil from the previous cookings are present in my new cookings? Is there carcinogenic stuff in the old oil?
You have a couple of potential issues, one possibly dangerous, the other has to do with flavor/quality control.  First, by not washing your cooking vessel, you leave the potential for bacterial growth.  This would be especially true if there is some down time (even a couple of hours) between uses.  The quality issue is that over time residual oil is going to become rancid, introducing off flavors into your food products.  So, I would strongly suggest a wash in warm, soapy water, or the dishwasher, between uses.