This should not be instead of taking him to the veterinarian. It is recommended that after you bring him home take him to your local veterinarian within the first 72 hours for a more complete exam. Nose should be cool and moist and not running. Squeeze the nostrils to see if there is mucus present. If there is a nasal discharge or frequent sneezing this may be a sign of a respiratory tract infection.
Most breeds have a scissor bite which is when the upper incisors tightly overlap the lower.
Gums should be pink and healthy looking. Pale gums indicate anemia. He should have clean smelling puppy breath. Pinch the windpipe gently. This should not elicit a coughing spasm.