Where they fall apart, literally in some cases, is anywhere that involves a lot of stairs or a long walk on a hard surface, because the sole doesn't flex the way a trainer does and your feet will know about it by mid afternoon. In the shop, check how the wedge is attached to the sole underneath the shoe, not just how it looks from the side, because a lot of cheaper ones are glued rather than stitched or moulded properly, and that's the first place they go. Have a proper walk around in them, not just three steps by the till, since the platform height at the front matters more than the heel height at the back for comfort. Check the inside edge where the strap meets the footbed too, that's where blisters start on a shoe that otherwise feels fine standing still.
Wedges age in a particular way. The cork or rubber wedge itself tends to scuff and darken at the edges first, especially if you're walking on anything rough, so wipe it down rather than let grit sit in there and wear a groove. Leather uppers soften and mould to your foot over a season, which is lovely, but suede ones mark if they get rained on and need a proper brush rather than a wet wipe to come back from it. If they've got any kind of canvas or rope detailing, that's the part that frays first, usually around week eight of heavy wearing, so don't buy a pair with rope wedges if you're planning to live in them all summer. A shoe bag in your holiday case stops the straps creasing against everything else, and it's a small habit that saves the leather.
The difference between a good pair and a sad one is almost always in the wedge itself, a solid, evenly finished block rather than a hollow sounding one, proper stitched straps instead of glued trims that lift after a few wears, and a footbed with enough shape to stop your foot sliding forward all day. Buy on how the wedge is built, not on how good it looks on the shelf.