End sentences with a preposition if you like. Rethink using Roman numerals for headings. Drop your citations to footnotes. Don't use Times New Roman (or Courier, you heathen). Avoid intensifying adverbs.
Do not assume that your reader knows everything that you do. Use the Oxford comma. Be concise, as this dissent. (Was Hansmeier the clerk?) Forego obscure acronyms (scroll to page 31). Correctly order statutory construction arguments.
Review the basics.
I'll respond to one suggestion (surprise!): relegating citations to footnotes. If you follow the link, the idea is championed by none other than Bryan Garner (the guy who edits Black's Law Dictionary). It is an interesting idea. He gives examples. In those examples, footnotes are a good idea. But the better idea is not to write the sentences in his examples. They are horrible. As a criminal defense attorney, here's my problem with citations in footnotes: courts sometimes think we are full of shit. And the only way we are not full of shit is if our words and ideas actually come from somewhere. So I use citations. All the time. If I were to relegate those citations to footnotes, I would write really long briefs. Because the thing is, citations in footnotes only shorten briefs (or whatever else) if the briefs (or whatever else) do not have that many citations.
Garner notes that he has critics on this issue, including Justice Scalia and Judge Posner. Add Paul Clement.
Don't get me wrong, I'm not anti-footnote. Long citations should be footnoted. Among other things. And, if you decide to go with Bryan and Kirk, I won't hold it against you. But the key, at least for me, is to learn to write shorter citations. Do you need to cite to docket entry No. 1? Try D.E.1. Need a pinpoint cite? D.E.1 at 1. Page 47 of Volume 1 of the Record on Appeal? How about something like R1 at 47. Or maybe just R1 47. The Tenth Circuit's Rules unfortunately encourage long citations (page 106). But the Rules also encourage you "to include a footnote in the briefs at the point of the first record citation to confirm the citation convention." I call this a loophole.
The other stuff is spot on (although I have no intention of abandoning my Roman numerals just yet).
Dan's premise that courts sometimes think we are full of shit is correct, and motivates my reasoning to drop cites to footnotes. The footnote offers a venue for fuller exposition of the case quote. After presenting the rule in the text, a footnote provides a place to set out multiple cases in support of that rule, with all of the relevant language laid out for the court. Remember your third grade math teacher exhorting you to show your work? Kind of the same thing here. This block of quotes would kill the narrative flow in the text, but works just fine in a footnote. I'm not arguing that your brief should look like a law review article, with three lines of text above 3/4 of a page of footnotes, but full exposition of the language upon which you rely is good for your credibility.
Dan's other suggestion about shortening record cites is completely right. A hybrid of the approaches makes sense to me. Drop a footnote when you need, and leave short citations in the text.