The crossword solutions for the term 'THIN MARGINS' are 'NOSES' and 'HAIRS'. Thin margins refer to a situation where there is very little room for error or deviation. In this context, 'NOSES' and 'HAIRS' can be interpreted as having very little space between them. For example, when talking about noses, thin margins would refer to the small gap between two noses when standing side by side. Similarly, thin margins in regards to hairs would refer to the small space between individual strands of hair.