Hold it up to the light before anything else, that's what I'd say to you in the changing room. Embroidered dresses live or die on whether the thread sits proud of the fabric or gets dragged down with it, and you can feel the difference with your thumb in about two seconds.
Once you're actually looking, check the back of the work as much as the front. A good one finishes the threads off properly so nothing snags on tights or a chair leg, a cheap one leaves loose loops that catch the first time you sit down and start unravelling by the second wear. Look at how the embroidery behaves where the fabric moves, across the chest, round the waist, because stiff thread on a soft dress means it'll pucker and never lie flat again once it's been through a wash. Check the lining too, some of the prettier ones put all their effort into the stitching and give you something see through and flimsy underneath it, which is a horrible discovery halfway through a day out. And always check the weight in your hand before the mirror, because heavy embroidery on thin fabric drags at the shoulders in a way that no amount of adjusting fixes.
Where it stops working is anywhere you need to move properly. Embroidered panels don't stretch, so anything fitted through the body will fight you if you're reaching, bending, chasing a toddler or dancing with any enthusiasm. It's also not forgiving of quick changes of plan, the kind of dress that needs its own hanger rather than getting balled into a bag, so it's the wrong choice for travel days or anything where you're living out of a case. I've got one that's beautiful and utterly useless for a long train journey because the stitching across the lower back makes sitting for three hours genuinely uncomfortable.
Where it earns its spot is anywhere slightly dressed up but not black tie, a wedding in a marquee, a long lunch, a birthday where you want to feel like you made an effort without looking like you tried too hard. It suits the warmer months best, spring through early autumn, because heavy embroidery under a coat just adds bulk you don't need. Keep the rest of the outfit quiet. Patterned tights, busy jewellery, a bag with its own hardware, all of it competes with work that's already doing plenty, and the dress ends up looking cluttered rather than special. Plain shoes, a simple bag, maybe one good earring, and let the stitching be the only loud thing in the room.
If I were starting from one, I'd go for cream or white first, because that's where you really see the quality of the thread against the fabric, nowhere to hide a bad job.