I'm sorry to hear about your rejection, but if it's any consolation, I met the admissions director during an open house last year and she mentioned quite often that HGSE is searching for passionate individuals dedicated to education and want to see that aspect somewhere in an application. She also said that the admissions committee doesn't categorize applications by GPA or GRE scores but examines each file holistically. Hopefully that'll help give you an idea of what they're looking for.
Anyways I was accepted to their Language and Literacy program. I'm currently finishing up my senior year in a 4 year B.A. and multiple teaching credential program at a state university, which means I've been working in elementary schools since my freshman year and am currently doing student teaching. I have a lot of volunteer experience in the community, having worked 3 years volunteering at a children hospital's on-site school program, 2 years working in an adult literacy program and 2 years doing leadership work with fellow literacy volunteers. I had a fairly strong SOP, great LORs, my GRE scores were decent (V600 Q680 A5.5) and my GPA is ok (3.70 CUM, 3.94 UPPER). One of my LORs was from a HGSE alumni, although I'm not sure what effect that had on my application, if any. Also the fact that I'm fluent in another language besides English helped me when applying to Language and Literacy (according to my alumni professor), but I'm not sure how that factors into other programs.
As for potentially negative qualities, I am young (I was 20 when I applied), lack any solid teaching experience in my own classroom and don't have any research experience.
Tuition and fees come to be around $37k, with living expenses being estimated around $20k.