"Ich führte den Hund in den Ort."
Would "I walked the dog..." be appropriate for "Ich führte den Hund..."?
No. it would not. "Ich führte den Hund..." really does mean leading (or dragging ?) the dog. To go for a walk with a more obedient dog one of the choices would be "Ich ging mit dem Hund spazieren"
What is the more correct translation- "I led the dog into town" or "I led the dog in the town"? They are similar yet have different meanings.
The given translation is correct. If you are leading the dog inside of the town (as in staying in the town the whole time, not as in coming from the outside and going into town) you would use dative: "Ich führte den Hund in dem Ort."
I understand about the accusative case but not about the meaning of 'Ort'. Sure, 'Ortscaft' means 'village' but Ort?
I agree on the use of the accusative case here but I think the translation is incorrect. The word 'Ort' means place or site. There is a word "Ortschaft' that means 'village'. A better translation would be 'I led the dog to the site" (or the place, or the spot).