Dotard – someone who is weak-minded or whose age has impaired his/her intellect.
Denotation – the literal, dictionary definition of a word.
Connotation – a meaning that is associated with the literal, dictionary definition. Connotative meanings usually are formed among certain social groups or as literary symbols. Connote means to signify beyond the literal meaning – Associations people make with a word.
Example: The literal, denotative meaning of a snake is a reptile with no arms or legs, etc. Connotative meanings are those associated with the snake: evil, untrustworthy, and so on. Connotative meanings can take the form of metaphors, synecdoche, metonymy and others. Or, a connotative meaning can be seemingly random. A chicken is a bird. Calling someone chicken implies they’re a coward. Coward is a connotative meaning of chicken.
A dotard literally refers to someone who is weak-minded; particularly someone older or experiencing senility. Connotative meanings of dotard could be a nursing home, old age, mental handicap, foolishness, a very slow driver who doesn’t use turn signals, someone who is helpless at some task, or other associations with lack of intellect or old age (bad hearing, old-fashioned).
Dotard seems to be a relatively neutral word although some of its connotations could be offensive to older people. Some connotations are based on stereotypes which means that for these cases, there may be no inherent connection to the literal meaning and in many of the cases where the connotation does arise from a stereotype, the connotation can be very offensive.