This is your chance to promote yourself despite your flaws. Your answer should point out a salvageable weakness. Admit that you're imperfect but have the gumption to work on your weakness because you are committed to being the best you can be. Explain that if you didn't perform at your best, you'd feel as if you were failing your program, and you find that unacceptable.

"I feel that my greatest weakness is my desire to socialize with every person I interact with. While this has never been a weakness in my life or education to this point, I realize I need to have boundaries with my patients to work effectively in a fast-paced setting. I don't foresee this as an issue for my Ultrasound Fellowship training because I've worked to get better in this area over my last two years of residency training. I will have to step out of my comfort zone a bit, but I'm ready for the personal challenge."