It seems everyone has a slightly different definition of what Down syndrome is. In order to simplify the answer, it easiest to start with "What is a syndrome?". A syndrome is a collection of clinically recognizable symptoms. In the case of Down syndrome, those symptoms are easily observed by most people. They include:
Hypotonia - decreased muscle tone
Nuchal fold - Short neck, with excess skin at the back of the neck
Low nasal bridge and facial profile
Microcephaly - small head, including ears and mouth
Epicanthal fold - Upward slanting or almond-shaped eyes, often with a skin fold that comes out from the upper eyelid and covers the inner corner of the eye
Brushfield spots - white spots on the colored part of the eye
Wide, short hands with short fingers, especially the pinky finger
Single palmar crease - a single, deep, crease across the palm of the hand. previously referred to as "simian crease".
Sandal gap - A deep groove between the first and second toes
While this list is not comprehensive and not all individuals with Down syndrome have all of these symptoms, identification of any of these characteristics at or near birth could indicate Down syndrome, but would require genetic testing to confirm.
In addition to the observable characteristics, there are several other potential symptoms:
Congenital heart defect
Strabismus (crossed or lazy eye)
Atlanto-Axial Instability (excessive movement between 1st and 2nd vertebrae)