Here would be the two big flaws they'll look for:
Little/No research experience -- Still be sure to get involved in the research of a professor in your university, and if personal commitments allow (you haven't mentioned being married or having kids) try to get an REU during summers. Hopefully even get a publication or two out of it -- and DO make sure to do some research presentations at conferences, even your "local" chapter. Showing prior, and successful, research is important to committees; it will show you "know the research gig" and are more likely to succeed as a graduate student.
Poor grades/GRE -- Obviously these factor in. If poor grades are early on in lower levels or in electives/gen-ed, it's of course better than if the poor grades are later on in upper-levels... but your best chances are with good grades throughout and a strong GRE. this will show you'll be able to complete core coursework successfully (before you really move onto full-time research for your dissertation).
Honestly, in my experience on a committee (in a department that had a few very highly ranked research areas and some recent Nobel Prizes awarded), we weren't really looking for young proteges. In fact, in my experience, our committee would be less wary of a slightly older student than a younger. An older student might have considered his/her career path more carefully, and be less likely to leave with an MS (or tank altogether). In short: We were looking to accept students with great records (preferably also from great schools) to result in an incoming class that would then have a high graduation rate (with the PhD degree, in a reasonable time frame), and be highly employable after -- in industry, national lab research or stable post-docs, etc. (i.e. not sticking around to post-doc for their own dissertation adviser). Maybe the top few acceptees to the program would be "young" proteges from Harvard, Yale and the like (maybe a year or so early) already doing research under Nobel-Laureates at their institutions and were hoped to produce top research in our program (perhaps looking to work under a Noble Laureate or a faculty member that was working on a problem that would perhaps become "Nobel-worthy")... but the one person I remember us accepting that was more young (by about 3 years -- and thinking of himself/herself as a protege-type) actually tanked and left before receiving the consolatory MS.
I also knew someone who attended undergrad at Cal Tech with one of those 12-yr-old proteges -- and, over fifteen years later (after successful graduation from Cal-Tech) that student was still working towards a PhD at the institution the student next attended (after a period of tanking). That would not be viewed as a success in our graduate program.