Unfortunately, there are no obvious outward signs of periodontal disease until it is VERY advanced. The earliest sign is inflammation (redness or swelling) of the gums. This is generally accompanied by a buildup of plaque and calculus on the teeth, but unless you are looking for these changes (see above, Is dental disease really a big deal?), they are not noticeable.
As periodontal disease progresses, the infection will worsen. The next signs within the mouth are receding gums or loose teeth. This increased infection may result in bad breath or blood on chew toys; however, this should NOT be relied upon for diagnosis. If your pet has bad breath or you see blood on toys, it is almost a sure sign of advanced periodontal disease requiring a trip to the veterinarian.
Late signs of periodontal disease include nasal discharge (blood or pus), eye problems, facial swelling or a jaw fracture.