With most of the nasal bones compacted, brachycephalic dogs tend to have trouble with the way their eyes seat in their heads.
First, recognize the prominence of the eyes on these dogs. The boney eye sockets are very shallow. This means that any blow to the back of the head, even a fairly minor one, can cause an eye to pop from its socket and require surgical replacement. This can happen also with too much pulling against the leash if the pet is wearing a collar. You may wish to consider a harness for your pet.
Sometimes, the eyes are so prominent that the lids cannot close all the way over the eyes. This will lead to irritation and drying of the center of the eye unless surgical correction is performed. If you cannot tell by watching your pet blink, watch as your pet sleeps. Dogs who sleep without closing their eyes all the way could do with surgical correction. Eyelid problems are common in these breeds. Look for persistent wetness around the eyes. In some dogs, the shape of the eyelids prevents normal tear drainage and there is an overflow. This problem cannot be corrected surgically and is not uncomfortable for the pet; however, there is a more serious condition which looks similar. This second condition involves the rolling inward of the eyelids such that the lashes rub on the eye. Surgery may be needed to correct this problem.
Chronic irritation will show as a pigmented area on the eye surface, especially on the side nearest the nose. This is hard to see without a bright light but if it is noted, a search for the cause is warranted. Depending on the location of the pigmentation, surgery may be recommended.