For forensics - excellent forensic psychiatrists are excellent clinical psychiatrists. So they want to see strong letters of recommendation highlighting your clinical skills. Strong writing skills are a must and most every program will have you submit writing samples - either forensic reports, an admission note or intake, or scholarly papers are evidence of your writing skills. Showing an interest in the field of forensic psychiatry is obviously a good idea. However, it is not necessary to have done forensic rotations (and probably not a good idea to do many if you are gonna do the fellowship anyway). I didn't do any clinical forensic rotations, was quite anxious about this, but to my surprise was quite highly sought after and it never really came up. I did however have other forensic related activities on my CV that showed an interest in and commitment to the field. I did receive comments about my publications and presentations - this shows you are putting in extra effort, having writing/presentation skills, and have some self-discipline and ambition - and thus will be looked upon favorably.
No one cares about USMLE scores at this juncture. Only one program I applied to asked for PRITE scores (which have been phased out this year). However it doesn't hurt to mention it if you scored consistently in the 99th percentile. Winning awards can be looked upon favorably. In forensics, the Rappeport Fellowship is THE award for residents. the American Academy of Forensic Sciences also has an award for residents I believe. The APA has a number of fellowship programs (public psychiatry, child, leadership, SAMHSA Minority/Diversity Leadership) which provide some training in leadership/advocacy and get you assigned to a council. It would be extremely favorable to your application to serve on the Council on Psychiatry and Law of the APA. Some forensic fellowships are keen on producing the next leaders in the field (and forensic psychiatrists often assume leadership and/or administrative positions) so it certainly wouldn't hurt to do things such as be the RFM representative for the state psychiatric association, or a representative for the state medical association, or serve as APA resident rep to the AMA, or on the RRC for the ACGME etc.
But as said above - by far the most important factor is performing well in residency (not so much what you know, but demonstrating you're a team player, have a professional work ethic, are dedicated to your patients, teachable and capable of teaching others, able to reflect on your strengths and weaknesses, open to feedback and constructive criticism, and constantly striving to improve). You don't want to be taking on additional responsibilities if you can't cope with the basic responsibilities of residency training. Also, if you have no interest in availing yourself of other scholarly opportunities, it would be entirely miserable, and I certainly wouldn't recommend doing these things simply for the purpose of applying for fellowship. I however found that the "additional" stuff was really the highlight of my residency training experiences even though it meant a lot of additional work.
Many forensic programs, particularly on the west coast fill by early summer. I applied beginning of April of my 3rd year and the west coast programs were all accepting applications already - this is not true for the East Coast. The forensic psychiatrist at my program told me I should apply in July. If I had listened, I would not have got the fellowship I wanted. This means if you wanted to go to Harvard or NYU for example (just picking random NE fellowships), you would effectively have to forgo applying on the West Coast. You may consider doing a forensic elective at the program you are interested in your 3rd year so you can get a better sense of the program and you will likely interview there and then and they will offer you the position.
But it's usually not too difficult to find something. As Phil Resnick told me "we get about 50 applications, and the ones that can speak English and write in English are invited for interview". The bar is low.
I will also mention forensic psychiatrists can be quite formidable, intimidating creatures. But if you rub some catnip on yourself, you realize they're püssy cats.
