I clean reedplates, mouthpieces and plastic combs using an old toothbrush and toothpaste where necessary- it's mildly abrasive and of course totally safe, not to mention fresh-tasting (though I avoid anything too minty).

Though I have a couple of Hohner chromonicas, I tend to steer clear of wooden-bodied harmonicas with nailed-on bits because they're just too tricky to maintain.