"Is John ill? He's lost a lot of weight."
"Yes, he's rather slender these days, isn't he?"

I can't see what is wrong with the 2 sentences above so I would be most grateful if someone could help me with the grammar.

Many thanks in advance
Emotion: smile It seems Ok to me too.Emotion: smile
It's unremarkable for dialogue, but if you have an exercise that says there's something wrong with it, then my guess would be that there's an objection to the use of "he's" to mean both "he has" and "he is" in subsequent sentences.

In formal writing you'd be advised to give the full (unabbreviated) form. It could be argued that having interpreted the first as "he has" (based on the rest of the sentence), the reader may be tricked into taking the second to be the same, thereby having to hesitate and re-scan when no verb follows.