......So my question is. Does it ever get to a point where a car is going to fast and the sheriff, cop, ST is just like "oh well maybe some other patrol car will get him" .....
I wouldn't say it's so much of "oh well", but rather, the officer will terminate for safety reasons (violator, officer, and public). When pursuing a vehicle you need to constantly weigh the risk of continuing the pursuit versus the risk of allowing the suspect to get away. In the example you mention the initial violation was speed. Now with the car being a Z06, it's a pretty good guess that the only reason the car was driving that fast is because it is a Z06. Does that make it okay? No, but it's not likely to have been someone fleeing the scene of a violent crime (though not completely out of the question, just not probable). So the officer needs to ask himself/herself if having 2 car now running 100+ is worth a a speeding ticket. Depending on traffic volume, road conditions, weather conditions, ect, it may simply not be worth it. Now if that car had just been reported fleeing the scene of a shooting, or armed robbery then yes, you'll push a little harder to catch it because the risk of letting them get away is greater than letting a speeder get away.
So to answer the question in short form. Yes there are times an officer will let a car go and hope someone further down the road will catch it.
Been wondering about the dogs too. Do you guys use the same dogs to sniff for drugs, bombs, track people etc? Or does each dog get trained to do it all?
Our dogs are all dual-purpose dogs. They are drug and apprehension, bomb and apprehension, drug and search/rescue, etc, etc. They've all got 2 things they're trained for.