The biggest problem with a design that "just doesn't feel right" is that "feeling right" is a vague and unquantifiable condition, meaningless and self-defeating. "It works for me" is a phrase every designer should write in bold letters on a big sheet of paper, then burn and never think of saying again.
Any design has a purpose: to say something effectively to a particular audience. The first step, then, is to be certain that you can clearly state the purpose of the piece. Sometimes just doing that will reveal what needs to be fixed. There's a bit of a trick to this, but it's not hard to learn. Once you have the message and the purpose clearly in mind, you "switch hats" and look at your design as one of its audience. (Say it's a car ad -- look at it as if you were the kind of person who buys that kind of car. Take their viewpoint.) You'll sometimes be amazed at what you can suddenly see that was invisible before.
The next step is to look at what "doesn't work" or "doesn't feel right" and articulate precisely why. This might take a bit of work, and you might have to borrow another pair of eyes, but as a designer this is probably the finest skill you will develop. When you can turn "it doesn't feel right" into "there is not enough contrast between the text and the background, so it looks unimportant" or "this is an ultra-modern product and Goudy is early 20th Century" or "the design leads the eye out of the frame instead of onto the product image" you will have conquered the problem simply by stating it clearly.
What not to do: ask for opinions and accept vague answers that begin "I think...", because they will lead you in circles and you will be no closer to your goal of a design that talks to the right audience and says, effectively and clearly, what the client needs to say.
One of the very best statements of this principle is this article by John McWade, from the Before & After blog. Highly recommended reading for any designer.