Both of the H.C. patrol cars get heavily damaged --- hood blown away, fenders torn off, dented/scraped doors, etc. --- during the start of the final chase, yet when they later are seen in Chickasaw County, both cars are fine again except for a missing hood.
In this episode, the balladeer mentions how it's hard to set up a proper roadblock when Chickasaw county only has one police car. A few scenes earlier, however, Sheriff Little crashes his car into a muddy ditch. Since it is impossible for a car to be towed out and reappear this quickly, it's safe to assume that the country does in fact have more than one patrol car. And indeed, in other episodes, Sheriff Little sometimes radios his officers to come and assist him and/or to drive around and keep an eye out for a certain suspect, so this indicates that there must be several patrol cars available to Little's force.
J.D. would not be able to legally foreclose on the Duke farm merely because he had just then put a lien on it, especially since the Dukes actually had the necessary cash, and so the payment could still have been made within a few days at most of when Bo and Luke were trying to rush into town and pay it. J.D. would have had to wait a good while after the first lien was placed to be actually able to foreclose on the property.
Bo and Luke don't bother getting a receipt from Boss Hogg for their property-tax payment; they simply hand him the money and run off again. The Dukes would never neglect to get a signed paper receipt from the conniving and devious J.D., especially since they knew that he was actively trying to stop them from paying their taxes at that time, anyway.