The thing that matters most with a crossbody bag is the strap length and how it adjusts, because the difference between it sitting at your hip and sitting right under your arm is about two centimetres and that's the difference between it being useful all day and you fiddling with it on a train platform. I want a strap I can shorten right down and lengthen right out, with a buckle that holds once I've set it, not one that slides every time I shift my coat.
Where it falls apart is when you're already carrying something with a strong shoulder line, a structured coat with a defined shoulder seam, or anything with a big collar or scarf that the strap has to fight its way across. It also looks wrong paired with another bag detail doing the same job, so a belt bag or a second strap bag at the same time is just too much hardware in one outfit. Keep the rest of what you're wearing fairly plain round the shoulder and it sits properly instead of getting lost in folds of fabric.
The one mistake worth avoiding is buying it unadjusted and leaving it, assuming the length shown on the model is the length that'll work on you. It almost never is, and it's a five second fix you do once and forget about.