If you are playing charming, you need to max both sweet-talk and rule bending skills AND get as much charm into your gear as possible. For example, your coat is a tough item, which does not help at all if you are trying to use sweettalking. There is a fairly cheap +charm coat in the Detective shop, or save any charm gear you win.
Smart gear doesn't really start helping til you have advanced smart skills like Footprint or Advanced hair. If you are still at basic smarts level, trade your smart gear for charm gear. It will help more early on.
Plus those featured mysteries are way harder than their "level" makes them sound. I did better on them after I had been solving ridiculouses a while. And even then, I felt less certain about my accusations. It still felt kind of like guessing, although I did succeed.