FWIW, re: wing struts, I was taught to check the strut fairings for cracks as well, on the idea that such could indicate something wrong with the structure... Not sure if that makes sense, but why not... Same thing with the main gear struts, since cracked fairings there could indicate overstress from a hard landing (fairings cracked by excessive flexing).
Re: nose wheel, was also taught to check for the presence of all necessary bolts (that's not in the POH). Bolt comes off during landing -> gear stays attached due to weight on wheel -> not spotted during preflight -> rotate -> you take off, your nose gear does not...
Has happened.