Although there is no mistake in the sentence in terms of grammar,there are problems in the choice of proper words.Negligence is a better choice than neglect,whereas mistake is more appropriate than mischief.So,the sentence should read as follows:Little negligence may breed great mistake.There are plenty of good examples in our daily life which exemplify the meaning or essesence of the sentence.If one does not pay any attention to some minor errors in learning English,these minor errors will accumulate over time,and when the final exam comes,these accumulated minor errors will come back to haunt him or her to the extent that s/he will fail the final exam.Therefore,an error is an error,it would be better to correct it right away.So there will be no accumulation over time so as to avoid the big disaster at the end.
A little neglect may breed great mischief.小不忍则乱大谋.