Mr. Turveydrop, the elder, is a most unusual person. What exactly is his mental condition? Is he a healthy person? Is Dickens being facetious?

Turveydrop is definitely there for a good laugh. However, Dickens uses him to, again, criticize London's society members whose primary concern is how they appear to others, and who may have little else to offer. Turveydrop is a fairly shallow character whose son is expected to take care of him simply to support his need to appear a certain way.