My son is a picky eater - he doesn't like green vegetables.
Tips
usage
Near-synonyms: 挑食 (tiāoshí) - picky about food, very common in mainland; 嘴刁 (zuǐdiāo) - discerning palate, can be neutral or positive (a refined eater). 挑嘴 lands in the middle, slightly negative but mild.
mistakes
There is a separate reading 挑嘴 (tiǎozuǐ, 3rd tone on 挑) meaning 'to sow discord by tale-bearing'. The food-picky meaning takes 1st tone - tiāozuǐ.