Does bad breath in an infant indicate anything serious?

Possibly. Bad breath is not typical in an infant and could have many causes, most of which are not serious but could require intervention. Your child should be examined by their pediatrician to determine the cause of their bad breath.
It's doubtful. Bad breath or halitosis may be related to several causes: regurgitation, sinusitis, throat infection, infected adenoids, poor dental hygiene, or even a foreign body stuck in the nose, just to name a few. Whether the odor is persistent or recurrent sometimes gives clue as to the source. However it is doubtful that bad breath is actually dangerous.
Possible. If your baby looks well you can check possible source of the bad odor, such as the use of pacifiers, mouth sores or any other signs of infection, thumb sucking, nasal blockage or foreign objects obstructing the nose can be the cause.