What's the meaning of the paragraph?

It means "I will monitor my thoughts for illogicality and not use ridiculous excuses with respect to my personal hygiene".
Starting to slip implies both physical and mental health.

Thanks!

It also means allowing a worsening of in personal standards.

I will start paying attention to myself. (How I look and feel, especially my personal grooming habits)

When I stop thinking that I need a shower because
(I smell so bad that even plants would die from the smell if I walked past them)

then I will know I'm starting to slip (revert back to my old ways of not taking care of myself)
.