My biggest beef is with Ori-peis, the mix between pugs and Shar-peis. Ori-peis were originally developed to eliminate the health problems of both parent breeds, like skin and eye problems in the Shar-pei. The original breeder liked Shar-peis but wasn't so fond of vet bills ... so, rather than breed healthier, she made up a new breed. The result is a muttpuppy with a whole lot of issues.
Dog Breed Info.com can give you the Ori-Pei's brief history, followed by an owner's testimonial that's worth a look. Their dog's suffered from not only cherry eye and entropion (eye "tacking"), but a respiratory infection too (hello, pug genes). Here's some other testimonials from owners on this forum:
"my nieghbors ori-pie has horrible eye problems. She had to have surgery at 4 months because fur was growing on the underside of her eyelid or something similar to that." (This is likely entropion: the eyelashes turn inward.)
"... Yes, just like a Shar pei, we had to get his eyes tacked twice before they would keep the eyelids from hurting his eyes. And just like humanes, my dog does have allergies. When my husbands acted up, Willies act up. ... They are kind of expensive at first but he was well worth it." (Allergies is another common problem in Shar-peis.)
"No complaints until Saturday when he began having grand mal seizures. Scary stuff. Now he's on meds and we're praying they continue to work for him (so far so good...no seizures since Sunday). He's got no underlying medical causes according to bloodwork & ultrasounds, so it looks like he has epilepsy. This seems to be something more common in the pug line but uncommon in shar peis. He's neutered, of course, so he won't be passing this along, wherever it came from. He's also had to have Cherry Eye surgery."
And people love these dogs!
It's not ethical to breed a pug to another breed, because they have so many breathing problems, or to cross-breed a Shar-pei, because of their eye and skin problems. Putting these two together only gives you a train wreck of health issues, yet people clamour for more!
And that's not my only complaint when it comes to Oriental dogs. What the heck is up with all the Chinese crested mixes? Why are people cross-breeding dogs with such obvious health problems? This one is STARING YOU IN THE FACE. Okay, so cresteds generally are pretty healthy, but you've got to be prepared to take good care of your dog's skin to keep it that way. Chinese cresteds are prone to breakouts of acne, and some can develop dry skin, which means treating them with special weekly baths. Then there's the temperature to be aware of... And those are only the skin problems. Some mixes favour their hairier parents, but plenty don't. Even breeding a "powderpuff" crested is no guarantee.
Also ... they're really ugly.

What is with all the tongues hanging out the side of the mouth, by the way? -- and don't even get me started on the Japanese chin mixes or we'll be here all day.
Wake up people. Your muttpuppies never come out looking and acting and ... being as healthy as you imagine they will. STOP RELYING ON HYBRIDS TO MAKE YOUR DOGS HEALTHY.
Normally I don't mind people buying [certain] designer dogs so long as they come from very, very responsible breeders, but people who mix breeds like the Ori-pei have no excuse. It's inethical, there are way too many health problems to consider, and that means there are no responsible breeders out there. We need to STOP creating these and focus on breeding healthier in the parent breeds. So steer clear of the Ori-pei!!