Because dogs are carnivorous it's extremely difficult to farm them in a cost effective manner. The only country that farms dogs is South Korea and the conditions are squalid.
Dogs are not prey animals and so react aggressively to handling/transport in a way that sheep, cattle etc don't as they can be herded. This means that these practices result in much poorer welfare for dogs. The consumption of dogs is not regulated and so their slaughter methods are usually very inhumane, even compared to other species. International guidance exists for the slaughter of livestock animals under the OIE but doesn't apply to dogs.
Because dogs are usually not farmed (and cannot be famed efficiently for a number of practical and economic reasons) consumption of dog meat relies on theft of pets/guard dogs to supply the trade, which is illegal, ethically problematic and can be distressing for owners.
Dogs transmit rabies and a number of people have died from rabies after consuming dog meat. (Again not a problem with other species)
Dog thieves have created significant conflict and violence in countries like Vietnam when they steal people's dogs, leading to some human deaths. In China, dog thieves often kill dogs with an illegal poison called tetramine. Tainted dog meat has then resulted in the death of consumers. These aren't problems that exist with the consumption of other meat.
Because dogs are stolen for the trade (illegal), often cross international borders (illegal without proper rabies certification) and are slaughtered inhumanely (unregulated), and because the sourcing and consumption of dog meat risks human lives. I'd say that eating dog meat poses fairly unique legal, ethical and welfare problems that don't exist for other species.