Not inherently sexual, but in Issue #2: The Unfamiliar, a supernatural being with a humanoid body appears, sporting a pair of bare breasts. The naked figure appears again in Issue #14: What the Cat Dragged in. Later, in Issue #10: Food Run, a goblin-like critter is featured that bears a tiny intact penis. All of it rather harmless though.
[Stray] A dog's ghost mentions they were "not dead yet" when they were buried. It's ambiguous if they were buried alive or if their ghost was stuck underground all that time.
["Lost"] Focuses on the ghosts of drowned animals. The final page depicts their remains in detail. There is no ambiguity to what happened and I'd advise skipping this issue if drowning is distressing for you.
Several characters experience trauma and anxiety throughout the series, though none so much as Jack, who becomes faint and paralyzed in one instance, alongside frequent and recurring nightmares.
[The View from the Hill] Discusses the differing beliefs of the animals, and the fear that their friend group may be split up in the afterlife as a result.
Sadly, a handful of cats meet their untimely end throughout the series. Avoid Issue #5: The Gathering Storm, Issue #6: Lost, and Issue #14: What the Cat Dragged in. Fake-out deaths involving cats are also present in Issue #3: Let Sleeping Dogs Lie and Issue #7: Something Whiskered this Way Comes.
Thankfully, no dogs are pitted against each other for sport, though the protagonists more often than not have to engage in melee combat with one or more aggressive entities-- sometimes other dogs.
Ace is bitten by a werewolf early on in the series, but instead of it flaring up once a month, he seems to fight it and keep it under control unless one of his friends is in mortal danger. For instance (to my recollection) a human sees at least one of the dogs talking, and dognaps the beagle. Ace gives chase, but is badly hurt, and has to "wolf-out" in order to complete his rescue. This is the only time (so far) that Ace's condition is mentioned again. (so far)
Fire spells are a staple of the series, and are often used in fight sequences. In addition, "The View From The Hill" focuses on a herd of sheep who died in a fire.
In Issue #6: Lost, not only are several young animals' corpses shown, but the human teen that abducts, tortures, mutilates, and eventually drowns the infant pets is killed by the protagonists. (As he deserved.) In Issue #14: What the Cat Dragged in, a cat's adolescent children pass away while dissipating into skeletons after being freed from a curse keeping them alive.
In Issue #6: Lost, a mother dog who discovered several deceased young animals-- including her own pups-- commits suicide by plunging herself into the waters to be with them and provide their spirits the motherly comfort that was stolen from them.