The term 'SLIGHTEST COMPLAINT' can be broken down into two words, 'SLIGHTEST' and 'COMPLAINT'. The word 'SLIGHTEST' means the smallest amount or degree, while the word 'COMPLAINT' refers to an expression of dissatisfaction or annoyance. Together, the phrase 'SLIGHTEST COMPLAINT' implies that even the smallest amount of dissatisfaction or annoyance should not be ignored. This phrase is often used to emphasize the importance of addressing any issues that arise in a timely manner.