There are five things that you can do a better job at brief writing. None of these involve grammar, research, or bluebooking. I assume that you are already tending to that.
1. Master the Facts and Craft them into a Compelling Story
The law matters, but it matters less than you might think. There is not a "case on point" that the court cannot construe as "off point." If you are the appellant in a criminal case, the law is likely against you anyway. There is no case or statute that matters without an emotional hook. The hook gives the court the desire to rule with you. The law gives them a way. The statement of facts is the most important part of the brief. Make it compelling. It should get about seventy percent of your attention. Before you can make the facts into a compelling story, you must know them virtually by heart.
Free the facts from the transcript. If you are trying to learn the facts the day or even the week the brief is due, you will not succeed. If you are trying to work from the transcript, you will dig facts out when you should be storytelling. The trial transcript does not tell a story. Witnesses were called at trial in the order they were called for reasons other than the story. The expert witness who did the autopsy was only available on Monday, so the transcript begins with dry recitation of a body being examined. The 911 operator was called on Tuesday morning at 11:48 because the judge asked the State to call a short witness just before lunch.
Take the transcript and reduce it down to a summary with specific page cites. Work from that summary. It will liberate the facts and make your statements of facts more compelling. However, you are not done yet.
Pay attention to storytelling. A story will keep the judge or law clerk interested. Want some tips on storytelling? Pick up a copy of Robert Mckee's book on screenwriting titled Story. Many of McKee's principles work for a statement of facts.
2. Narrow the Issues
From the Court's perspective, the trial courts generally get things right. If you are fortunate, you will convince them that the judge made one reversible mistake. The odds of that happening go down, not up, with the proliferation of issues. Except in rare circumstances where the judge really was as bad as you thought he was, there are no more than three real issues (three is really pushing it). You water them down and will not be taken seriously if you fill the brief with issues. Find your best argument, and develop it.
3. Pay Attention to the Design of Your Brief
Design and appearance is important. Sight pollution will garner an overworked law clerk or judge very little time on your brief. Leave plenty of white space. Group similar items together. Pay attention to the font you choose. Take a look at this article on the topic of design in the appellate brief. In short, do not clutter the page with words just to meet your page limit. If you have narrowed the issues you will not need all that space.
4. Get a Second Computer Monitor
The late Randy Pausch said that the difference between a single monitor and a double monitor is the difference between working at a desk and working on a tray table in an airplane. For writing a brief, it is the difference between a typewriter and a computer. With a two-monitor work station, you can have your brief up in one screen and your research on another. If you had a third (I don't yet), you could put the law on one screen, the record on another, and your brief on a third. It makes a difference to scroll through or search through an electronic transcript versus a two-thousand page record on paper spread all over your desk.
5. Listen to Your Client, but be Her Lawyer
Appellate law is a specialty, and the best issue may seem obscure to your client. Your client's pet issue may be the moment where he felt most mistreated by the judge or betrayed by a witness. For an incarcerated client, the best issue may be the one unearthed in a donated book in some prison law library or suggested by a "jailhouse lawyer." Listen to your client, but do not be pressured into hurting his case to placate him. However, really listen to your client and develop a relationship of trust if at all you can.
None of these things will work if you don't work early. You can't establish a relationship, master the facts, and craft a compelling story the week before the due date. You can't design the brief and eliminate the weak issues hours before your due date. These five things will transform your brief writing if you take the time to do them.