Single speed cyclocross is a beautiful thing, as very little can go wrong. A good chainline makes chainsuck irrelevant and you never never ever stack because you missed a shift going into a barrier and forgot to get off your bike. With a 135 spaced rear hub built without dish, the probability of tacoing your wheel is extremely low.
Being a competitive single speeder, to me, means finishing at as well as (or at least nearly as well as, and sometimes much better than) you would have on a geared bike. This obviously can be very course-dependent (see below). If you want to be competitive as a single speeder in cross may I suggest the following:
Be a good or great runner. There will be parts of the race that you can ride in the beginning that you will be forced to run toward the end. To be competitive you need to be able to run as fast as or faster than those who choose to ride that part of the course. You should also be able to run faster than those around you on the run ups. On anything that points uphill, you need to be going faster thatn anyone around you, because you will get your butt whipped on any downhills that are smooth or long enough to allow pedaling. If you are one of those people who walk up the runnups the last few laps, you will get eaten up and spit out on a single speed.
Choose a good gear. This obviously is the key. You want to chose a gear that lets you not get dropped too badly on the flats and allows you to ride as much as possible on the hills. If you have to get off your bike you better be able to run well (see above). I find a 2:1 is best for me. Although I could see going a bit higher as I get faster. Travis Brown runs a much higher than 2:1, but he is a machine and a half. Being a mere machine, 34:17 works well for me, although I am going to try some races in the 34 16 soon. i think if you are running anything less than 2:1 you need to be able to spin like a mad bastard, consistently through the whole race.
The key to most single speed cross races are the start, and the end. (and the middle too). Most large field cross races (UCI style) start on a big flat open area like a track or a paved road so that there are no bottle necks by the time you get down to the skinnier trails. The start is important. Spin like a freak, and then spin faster. If you don't you will be in bad shape position wise and you will probably get caught up in the inevitable bottlenecks anyway and loose a ton of time.
The end is key as well because this is when everyone around you starts to zone out and spin a tiny gear on everything. You don't have this luxury, the lack of gears makes you a better cross racer at the end of the race. Make sure you are fit enough to beable to maintain a good effort through the end of the race or you loose your key advantage over those on gears.
Know your course well:
If you have a sadistic jungle cross race promoter in your area, he is your friend. Nothing can even the odds in a race more than lots and lots of run ups and single track descents that prevent pedaling. Especially if they start up hill. Especially if people use the word insane to describe the course.
Hilly courses that have lots of up-and-down and barriers are also your friend.
Rain, mud and unbelievably crappy weather make your job easy. All you need to do is put your head down and churn, and then get off and run when it becomes to hard to churn. Everyone else will be flubbing their shifts, stopping to pull the chain out of the tiny space between the chainring and frame etc. Super cup portland last year could have been a huge waste of time for me. The course was flat and fast with very few run ups. Fortunately the course was covered in peanutbutter, ankle deep mud and puddles and after a epic single speed battle with some VP of such and such from an unnamed east coast framebuilder, I had my best finish ever. I finished 10th in the B's and based on my lap times, I would have been reasonably competitive on the A's (meaning no pro's would have lapped me twice and I would have not finished last and maybe would have finished in the top 2/3rds.)
Dry northern california winters are your enemy. As are promoters who go to europe and decide that for some reason that districts should be eurocross style with drafting playing an important role in the the final results. Any course that has 25% or more pavement and fast sweeping pedalable downhills is trouble. Just pretend it is a training race and work on your high speed dismounts. Try not to get in anyone's way when they lap you for the tenth time. Curse Europe and dry weather under your breath. But don't winge audibly, it makes you look silly.
If you want to race fixed gear cross, make sure you are comfortable with all sorts of flying dismounts and lots of off camber skidding stuff. Prepare to be utterly uncompetitive, but a crowd favorite. Someone (for somereason I can't find the email in the archives) mentioned that they ride their fixie off road all the time. This is fun and good and makes you a much better person. I think they mentioned that they like to run a higher gear on a fixed gear off road than with a coaster rake I also agree. I run my 65 inch gear on fire trails and (mild) single track in the Oakland hills and in SF often. It is a very good thing.