Error, mistake, blunder, slip, lapse, faux pas, bull, howler, boner are comparable when they denote something (as an act, statement, or belief) that involves a departure from what is, or what is generally held to be, true, right, or proper.
Error implies a straying from a proper course and suggests such guilt as may lie in failure to take proper advantage of a guide (as a record or manuscript, a rule or set of rules, or a principle, law, or code); thus, a typographical error results when a compositor misreads a manuscript; an error in addition involves some failure to follow the rules for addition; an error in conduct is an infraction of an accepted code of manners or morals.
Mistake implies misconception, misunderstanding, a wrong but not always blameworthy judgment, or inadvertence; it expresses less severe criticism than error.
Blunder is harsher than mistake or error; it commonly implies ignorance or stupidity, sometimes blameworthiness.
Slip carries a stronger implication of inadvertence or accident than mistake and often, in addition, connotes triviality. Often, especially when it implies a transgression against morality, the word is used euphemistically or ironically.
Lapse, though sometimes used interchangeably with slip, stresses forgetfulness, weakness, or inattention more than accident; thus, one says a lapse of memory or a slip of the pen, but not vice versa.
When used in reference to a moral transgression, it carries a weaker implication of triviality than slip and a stronger one of a fall from grace or from one’s own standards.
Faux pas is most frequently applied to a mistake in etiquette.
Bull, howler, and boner all three are rather informal terms applicable to blunders (and especially to blunders in speech or writing) that typically have an amusing aspect.
A bull may be a grotesque blunder in language typically characterized by some risible incongruity or it may be a mere stupid or gauche blunder.
A howler is a gross or ludicrous error based on ignorance or confusion of ideas; the term is used especially of laughable errors in scholastic recitations or examinations.
A boner may be a grammatical, logical, or factual blunder in a piece of writing that is usually so extreme as to be funny <a few historical boners … such as dinosaurs surviving until medieval times —Coulton Waugh > or it may be a ridiculous or embarrassing slip of the kind that results from a sudden lapse (as of attention or from tact or decorum).