error suggests the existence of a standard or guide and a straying from the right course through failure to make effective use of this.
procedural errors
mistake implies misconception or inadvertence and usually expresses less criticism than error.
dialed the wrong number by mistake
blunder regularly imputes stupidity or ignorance as a cause and connotes some degree of blame.
diplomatic blunders
slip stresses inadvertence or accident and applies especially to trivial but embarrassing mistakes.
a slip of the tongue
lapse stresses forgetfulness, weakness, or inattention as a cause.
a lapse in judgment
Word History
Etymology
Verb (1)
Middle English slippen, probably going back to Old English *slippan, weak verb cognate with Middle Dutch slippen "to lose one's footing, slip," Middle Low German slippen, Old High German pesliphen, pislipfan "to lose one's footing, stumble," intensive derivative of Germanic *sleipan- "to slide, slip" — more at slipper entry 1
Note: The Oxford English Dictionary, first edition, and Oxford Dictionary of English Etymology take the Middle English verb to be a loan from Middle Dutch or Middle Low German, though it seems equally or more probable that it is a native formation, as was Walter Skeat's view.
Noun (1)
Middle English slype, slipp "sloping landing place for a boat," noun derivative of slippen "to slip entry 1"
Noun (2)
Middle English slyp "edge of a garment," probably borrowed from Middle Dutch sleppe, slippe "loose end of a garment" or Middle Low German slippe, in same sense, of uncertain origin
Note: The earliest sense of this word, "edge of a garment," is first attested in the English-Latin dictionary Promptorium parvulorum (ca. 1440), in the entry "Slyp, or skyrte: Lascinia [for classical lacinia 'border of a garment, edge, hem']." Presumably derived from this meaning is sense 2. The meaning "scion, offspring" (sense 1 and hence sense 3) is first attested in Wynkyn de Worde's printed edition (1495) of the medieval encyclopedia De proprietatis rerum, adapted from John of Trevisa's 14th-century English translation. It is not clear how "scion, offspring" might relate to the other English meanings ("strip of material" > "shoot of a plant"?), or to the presumed Middle Dutch/Middle Low German etyma, which have no comparable sense. -- The word slyp is also attested in the sense "cleft, crack" in late Middle Dutch (the dictionary Teuthonista of Duytschlender of Gert van der Schueren, 1477); it has been suggested that this was the earliest sense, with "cleft in a piece of fabric" leading to the meaning "loose end of a garment." The noun slyp is clearly derived from an earlier verb slippen "to split," which may be a weak derivative *slippōn- (< *slib-no-) of a Germanic strong verb *sleiban- evident in Old English tōslāf "(s/he) split, cleaved," assumed infinitive tōslīfan (see sliver entry 1).
Middle English slyp, slype, slyppe "mud, slime," going back to Old English slypa, slyppe, slipa (masculine or feminine weak noun) "slime, paste, pulp," going back to Germanic *slupjōn-, zero-grade noun derivative from a Class 2 strong verb *sleupan- "to creep, glide" (whence Old English slūpan "to slip, glide, move softly," Middle Dutch slūpen "to creep, glide," Old High German sliufan "to slip, creep," Gothic sliupan "to slip (in), enter stealthily"), probably back-formed from an intensive derivative *slupp- (as in Old High German slopfāri "itinerant monk," intslupfen "to slip away, escape") of a hypothetical verbal base *sleub- "slip," perhaps going back to Indo-European *sleu̯bh — more at sleeve
Note: This account of the origin of *sleupan- is based on R. Lühr, Expressivität und Lautgesetz im Germanischen (Heidelberg, 1988), p. 352; her hypothesis is taken up in Lexikon der indogermanischen Verben (2. Auflage, 2001), s.v. *sleu̯bh-. As the author points out, this back-formation would have to extend as far as the ancestor of Gothic to account for the verb in that language.