MOTE. A particle of dust or chaff, or a splinter of wood that might enter the eye. Rendered as “speck” by NIV, the word is used by Jesus (Matt.7.3-Matt.7.5; Luke.6.41-Luke.6.42) in contrast with “beam” (kjv), “log” (rsv), or “plank” (niv) to rebuke self-righteousness in correcting small faults in others, while cherishing greater ones of our own.

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MOTE (κάρφος, G2847). A word used metaphorically by Jesus to denote a minor fault. The Gr. word refers to a minute bit of anything, like wood, straw, or even wool, that might be flying about and enter the eye (Matt 7:3ff.; Luke 6:41f. [RSV SPECK]). Jesus contrasted the minuteness of the mote with a beam that supports the roof of a building.

International Standard Bible Encyclopedia (1915)

A minute piece of anything dry or light, as straw, chaff, a splinter of wood, that might enter the eye. Used by Jesus in Mt 7:3 ff; Lu 6:41 f in contrast with "beam," to rebuke officiousness in correcting small faults of others, while cherishing greater ones of our own.