We just finished the specific aims page assignment in our professional skills course for PhD students (and, coincidentally, I had study section last week). Here are a few writing issues I see a lot that are easy to fix if you know to look for them. Make sure directionality is clear.
Instead of "X has a major impact on Y" say "X has a major *positive* impact on Y"
This issue can apply to high-level concepts or specific results; the statement "A is *negatively* correlated with B" is clearer than "A is correlated with B"

Here are some thoughts from a recent newsletter article I wrote that may be of broader interest. This is about the benefits of applying for awards, grants and fellowships and is primarily geared towards graduate students, postdocs, and newly independent investigators. 1/6 If you feel you are competitive and a good match for an award, grant or fellowship put your name in, or ask someone to nominate you, even if you are not confident you will receive it. Many of us sometimes sell ourselves short – you may be more competitive than you think. 2/6