Because Pugs have a relatively small gene pool the breed is known to suffer from quite a few hereditary health issues some of which are quite serious. These include the following:
Eye Disorders
Cataracts
Distichiasis
Entropion
Exporsure keratopahty syndrome
Keratoconjunctivitis sicca (Dry eye)
Progressive Retinal Atrophy (PRA)
Pannus
Pigmentary Keratitis
Corneal ulcer
Muzzle Problems
Elongated Soft Palate (ES)
Stenotic Nares
Intestinal Issues
Intussusception – male dogs under the age of 18 months
Leg Problems
Luxating Patella
Neurological Health Issues
Pug Dog Encephalitis (PDE)
Would you seriously even consider this when there are other breeds, and mutts around who that are know to be pretty much issue free? Sure, every dog is a gamble but consider the balance of risk.
From the same site Pets4Homes, on Parson Jack Russell breed info page
In good health, the Parsons Terrier can live up to 20 years of age, but usually average around 15-16 years old. Like the Jack Russell, it is a hardy and healthy breed of dog, and has very few congenital defects; however, pure white dogs can be prone to deafness
That is it, nothing else. No list of known problems.