Most recipes call for minced shallot in a basic vinegarette.  However, whenever I use it, the taste of shallot overpowers everything else in the dressing, leaving an aftertaste that usually lasts through to the next day.  I've tried reducing the amount of shallot, but no matter how little of it I add, it always takes over.  The problem is, I like the taste of shallots, and I think they taste great with greens.  I just want to eat a salad that tastes of things besides shallot.  So, is there a way to keep the taste of shallots in my dressing without it being the main course? 
There should definitely be an amount small enough to suit you. The tricky bit is that if you don't get it evenly distributed, you'll still have bites where you get a piece of shallot and it's too much.  A couple ideas to fix that:   puree your shallots, so you can thoroughly mix in a small amount that suits your tastes let the dressing rest for a day or two before using, so the flavors meld better simmer or heat the dressing, if the other ingredients can take it, to speed along the melding   If you get that taken care of, you should be able to then reduce the amount and find what you want.  You can definitely also temper the flavor as Dorothy suggests, but if it's the general flavor (not just the harsh notes) that's giving you issues, all that'll do is increase the size of the small amount that suits you. 