What do you do when you don't like the out come of a Commission?

[nakoothetauren.livejournal.com]

What should someone do when they don't like what the artist they commission has provided for them?

I've been in a situation recently where the artist I commissioned said that they where happy with what the made for me yet I was not.
I feel like they rushed the commission and this caused issues. I don't want to go into real details but I want to know if there is anything a customer could do about this?
There where things wrong with the drawing, the artist got things about the character wrong but they stated that they where trying to replicate the style of the characters souse material (In this case MLP). To me it was clear that they where not as the eye's in particulate where still in there own style.
I asked them to change the things I thought they got wrong and they said that they where happy with the work they did. There was no mention of changes costing more. This was for an Icon so there was no progress shown.
I've personally dropped the issue but I want to know what I could do if this happens in the future?

(I hope this is better worded, I'm not the best with explaining my self sorry.)