The main issue with the extremely brachycephalic breeds is finding a decent breeder who is doing all they can to produce healthy, sound dogs. On top of the usual requirements for a decent breeder (health testing, aiming for low COI, etc., etc.) you need to find someone who is actively breeding away from what the breed is "supposed" to look like.
There's a real problem with the breed clubs being in resolute denial that the shape the members want their dogs to be damns a high proportion of them to various conformation-related health issues, particularly brachycephalic obstructive airway syndrome. Recent studies have shown that breathing issues in brachycephalic breeds are chronically under-reported by their owners and this is likely the case because the snorting/snoring/noisy breathing/wheezing/low exercise tolerance/low heat tolerance/etc. is presented to them by breeders and breed enthusiasts as being not only acceptable but perfectly normal. Despite the breed being prone to it (as a direct result of their conformation) the breed club currently doesn't even mention hemivertebrae on their health page and there's no push for breeders to start screening their dogs.
There are always some individuals in brachycephalic breeds who manage to dodge the bullet as far as health issues go but the conformation of these breeds massively predisposes them to a range of conformation related health issues and the question really needs to be asked whether it's ethical to continue breeding them as they are when such a high proportion of them have compromised health as a result.
Bostons have the highest rate of litters born by c-section of any breed with a whopping 92%. This is because of dystocia due to foetal-pelvic disproportion i.e. another issue directly related to the shape they've been bred into: the large head and relatively narrow hips. Again, I think we should be asking whether it's ethical to have produced a breed so far removed from normal dog structure that it has almost lost the ability to whelp naturally.
The breed also has a major issue with genetic diversity, the current average inbreeding coefficient is 10% which is almost as high as what would be produced when mating half-siblings (12.5%). The Effective Population Size of the breed is currently dangerously low at only 36.78. An EPS of lower than 50 puts a breed at very high risk of heritable health issues as well as inbreeding depression which causes a general decrease in the health of the breed as well as negatively affecting litter sizes and fertility.
A responsible breeder of Bostons will be going above and beyond as far as health testing goes. They'll be doing everything recommended by the breed club (DNA test for hereditary cataracts, patella grading, BVA eye test) as well as x-raying for signs of hemivertebrae and DNA testing for limb-girdle muscular dystrophy. They'll be actively breeding away from the current conformational trends, aiming for longer noses with open nostrils, properly situated eyes, decent hid leg conformation (they've a tendency to be very upright behind) and normal tails. They'll be trying to establish a reliable ability of bitches to self whelp their litters. They'll be paying very close attention to the levels of inbreeding in the lines they're using and be trying to breed litters with COIs of as close to 0% as possible.
Unfortunately breeders like this, if they exist at all, are extremely hard to find. As in many brachy breeds most breeders seem quite content for things to remain just as they are 