I've only had to track down past taxis a handful of times, once because a (Chinese) friend was gouched coming into town from PEK, and the rest of the times because either myself or a friend left valuables behind. Believe it or not, recovery odds are pretty high. In Beijing, you generally either need a receipt or closed circuit video footage (cameras are everywhere) to pull this off because all of the taxis look the same. In Shanghai, in addition to the above, simply remembering the color of the taxi (this tells you the taxi company you need to call) and the drop off time/location is often sufficient.

In any event, it should go without saying that leaving valuables behind is best avoided, and that you should keep your receipts just in case your cell phone has a mind of its own.

With respect to circuitous routes, Beijing is idiot proof geography wise, and you can follow along with the map on your phone. If the driver does opt for a unique routing (e.g. 5th or 6th Ring to/from PEK), it's probably due to traffic issues, but if it starts to get too unique, simply speak up or point to your phone.