1570s, "wearing slippers or loose shoes," from slip (v.) + shod "wearing shoes." Sense of "slovenly, careless" is from 1815, probably from the notion of appearing like one in slippers, or whose shoes are down at the heels.
early 14c., "to escape, to move softly and quickly," from an unrecorded Old English word or cognate Middle Low German slippen "to glide, slide," from Proto-Germanic *slipan (source also of Old High German slifan, Middle Dutch slippen, German schleifen "to glide, slide"), from PIE *sleib-, from root *(s)lei- "slimy, sticky, slippery" (see slime (n.)).
From mid-14c. with senses "lose one's footing," "slide out of place," "fall into error or fault." Sense of "pass unguarded or untaken" is from mid-15c. That of "slide, glide" is from 1520s. Transitive sense from 1510s; meaning "insert surreptitiously" is from 1680s. Related: Slipped; slipping. To slip up "make a mistake" is from 1855; to slip through the net "evade detection" is from 1902. To let (something) slip originally (1520s) was a reference to hounds on a leash; figurative use "allow to escape through carelessness" is from 1540s.