How do I catch the seriously ill patients who seem fine?

You can triage most patients now, and the ones that scare you are the quiet ones, the truly sick who don't look it until it's almost too late. That worry is a sign of a good clinician, not a failing one. The dangerous cases are dangerous precisely because they hide, and catching them is the hardest part of the skill. The way you get better at this is pattern and suspicion. You learn the subtle signs that don't match the calm surface, and you build the habit of asking, what would I miss if I trusted how this looks. The seasoned ones aren't calmer. They're more suspicious of the patient who seems fine. After each shift, take one patient who turned out sicker than they first appeared and study what the early clue was. Collect those clues over time. That's how the deceptive cases stop slipping past. Every one you catch teaches you the next, and the pattern slowly becomes something you feel.