I am in the UK and stored everything in my attic which was rather damp and I didn't have a second thought about using my 4 year olds clothes for the new baby.
Everything was washed in Persil non-bio (a brand of washing detergent which doesn't contain cleaning enzymes, marketed as better for sensitive skin) at 60 degrees C and all checked for obvious mould spots or dirt that wouldn't come out - and thrown if they did.
My now 2 Year old had no ill effects from wearing second hand clothing and still continues to do so, even from charity shops and bought from random people. I very rarely buy anything new.
Mattresses are the main thing to worry about. It's advised definitely not to reuse them and I also replaced the Moses basket.
There is a link between mattress reuse and SIDS (cot death), so we are all advised in the UK it is best not to - although for a second baby in the same household, there seems to be debate on whether it is the same. (I cannot find evidence of that specifically but I remember from my own research previously there was a lot of discussion about it)
I could not be certain my moses basket was clean as it had been in the damp attic and it's not washable, so changed that. I am still using the cot.