At the end, when Squeaks, the elusive caterpillar that Dinky and Boomer chase throughout the film, turns into a butterfly, it's a reflection on the larger plot where the hunters and prey reconcile.
When Copper starts leaving his barrel to go play with Tod, Chief makes a point to tell him how upset Amos Slade will be about it. True to this prediction, Copper is put on a leash for his misbehavior. Before Copper started wandering off, what was the biggest difference in how Amos Slade treated Chief and Copper? Chief was always kept on a leash. He had been trying to warn Copper about losing his privileges the same way that he did when he was younger.
Chief is dramatically outshone in tracking abilities once Copper shows up. Old age? Not likely. Chief looks like a shaggy greyhound-esque breed or mix—lean, tall, long thin muzzle, small ears, no wrinkles. In other words, he's a sighthound. Sighthounds are bred for just that—flushing and chasing prey based on line-of-sight, working in tandem with the handler. Scenthounds like Copper have been designed through thousands of years of breeding to locate prey by smell alone. They're just built for different styles of hunting. Copper was always going to be better at the kind of tracking-heavy hunting style his master prefers.
Another bit of Fridge Brilliance is that those types of dogs are often used together.
Slade is completely taken aback when Tod and Vixey jump through the burning grass blocking their escape from the foxhole. Any wild animal would instinctively flee fire, but Tod was semi-domesticated, and had been by Widow Tweed's fireplace before.
The movie begins with the baby fox's mother hiding him and sacrificing her own life for his, Bambi-style. However, foxes almost never have a single cub. This mother wasn't just carrying her baby to safety. She was carrying to safety the only baby of the litter who survived the hunt.
Although it's more like Fridge Sadness: The end of the film pans out on Tod watching Copper from a hill. It was earlier shown that the widow drove what was possibly hours getting Tod to the reservation, meaning he traveled a long while to look at Copper and his old home one last time.
While trying to get Tod to understand the harsh reality that Copper, as a hunting dog, will have to become his enemy, Big Mama, Dinky, and Boomer show him Amos's shack of animal skins. At least one fox pelt can be seen. It's very possible that among all those skins is the skin of Tod's mother, and he might have been looking right at her (though if this is the case he doesn't seem aware of it, thank goodness).
Considering that Tod's mother seems to flee for MILES to get him to safety, and Amos' sheer persistence while hunting, this is sadly very possible.
Between the burning grass and Copper, Tod chose to try his luck by jumping through the flames. Copper used to be Tod's best friend, and now he became scarier than the fire.
Why did Amos Slade keep Chief on a leash but let Copper go unrestrained? It's all well and good to teach your dog to stay near your house on its own accord while it's still young, but shouldn't Slade have been personally watching him during this learning period? There are wild animals all around their house! A puppy Copper's size could geteatenif it wanders too far.
In the time period this takes place in, especially in a rural home, this would have been normal animal care. Doesn't make it any better or more sensible, but it fits the mentality of the time.
Adding to this, from what's implied, Chief did what Copper did and that's why he's chained up, so the reason why he might have been allowed to wander around probably wasn't because he allowed to wander around in a sense, just that he had to learn to stay on the property (how Slade expected to accomplish this without actively training Copper is Fridge Logic in itself) or that he expected Chief to keep him out of trouble (again, also Fridge Logic).
Is Slade going to be arrested for trespassing onto a game preserve? Hunting license or not, Slade was poaching all because of a petty vendetta.
When Tod is getting to know Vixey, Dinky and Boomer suddenly show up out of nowhere to watch them.
During the bear attack, Amos Slade struggles to reach for his gun since his foot is caught in one of his traps. The trap is clearly seen being held down by a post; it would probably take less effort to pull it out of the ground and go for the gun rather than try to pry the trap open.
Panic, most likely. Amos probably wasn't thinking rationally, and even as a man with obvious survival experience, it's quite possible that in the chaos pulling the post out of the ground didn't occur to him.