Mountain bike racing is a very competitive sport, and positions are closely fought over. Give yourself the best chance of that podium finish by making sure your bike is in tip top condition.

Things to check:

Wheels:

A slightly off-true wheel wont effect you riding dramatically, but in some cases can reduce the strength of the wheel or how well the wheel spins. Most importantly make sure your hubs bearings are greased and checked over, and make sure any snapped spokes are replaced. Also make sure your rims don't have any dents or dings that make puncture your tyres.
 

Forks & headset:

You will get more out of your bike if you take the time to set up your suspension to suit your weight, riding style and the course you may be racing. On rear shocks, especially for downhill racing rebound is likely to be the only thing you might adjust.... slower rebound for hard hitting tracks and faster rebound for tracks without drops etc.

Check the over-all condition of your forks, make sure the seals are in good condition and that there aren't any major chips or scratches to the stanchions - if so get a qualified fork technician at a local bike shop or at somewhere like TF Tuned to sort it out for you.

Keep the forks serviced fairly regularly, especially if they start to feel or sound not quite right. Set the preload, sag, rebound and any other adjustments to suit you, the track and your riding style.

Make sure you keep the headset regularly serviced, and make sure to clean it well at the same time. Check for play, if there is some try cleaning and greasing the bearings - if this doesn't solve it, you are in likely need for some new bearings or a complete new headset. If your not sure what your doing get a professional bike mechanic to sort out any problems for you.

The headset shouldn't feel stiff when turning the bars/forks.
 

Brakes:

A vitally important feature you will need for any mountain bike race. For most races you need to have 2 fully working brakes to be able to take part.

Whether you run hydraulic discs, cable discs or even v-brakes take time to inspect the pads, and replace them if the amount of pad left available has fallen below the MAX USE LINE.

Hydraulic brakes normally need a re-bleed every few months to keep them feeling sharp and to clean out the system from dirt or air bubble build ups.

Keep your disc rotors (or rims if using v-brakes) clean, and especially with disc rotors replace heavily scratched or cracked rotors.

Warped rotors can be straightened out using 2 adjustable monkey wrenches.... (see a tech tip coming soon)

Make sure your cable routing is good, and that there is no long bits of cable flapping around to get caught on obstacles.
 

Gearing/Drivetrain:

An important feature of any bike. Make sure you can access your full range of gears, and that the shifting is clean and quick, and that there isn't any ghost shifting.

Make sure to properly clean your drivetrain after every ride, and use water dispersant (like X-lite bikespray) to get water out of the cogs etc to prevent rusting. Keep your chain clean and 'lubed' (Finish Line make some fine bike lubricants).

Ghost shifting can be an major problem, losing you valuable seconds in racing if you are slowed up by not being able to select the gear you want, or by chain suck. If like me your not much good with setting up gearing get a qualified bike mechanic or someone who knows what there doing to sort out any problems you many have.

If your running a chain device make sure it is firmly built up around your crankset, and that there is no movement within it. Keep an eye on chain and chain ring wear.

Make sure your gear cables (both inner and outer) are in good condition. Slow shifting make be due to a slack old stretched cable. Make sure you cable routing is up to scratch with no 'flappy' long sections of cable to get caught on obstacles.
 

Controls:

For most races you must have some bar end plugs fitted to prevent any nasty impaling injuries. Fit them, now! Many companies including X-Lite, Hope, Royal Racing make bar end plugs for £15-20, they do the job and in most cases look the business.

Make sure your stem and bars are tightened and straight. Simple, but really a important thing to check.

Make sure you have your shifter(s) and brake levers set in comfortable reachable locations on your bars - set brake levers up according to whether you brake with one or two fingers. A good idea with brake levers and shifters is to do them up tight, and then back them off half a turn so that they can rotate around the bars in a crash instead of snapping.

Make sure on the race day your seat is done up tight on the seatpost, and that the seatpost collar is sufficiently tightened to prevent is slipping round.

Lock on grips are the best and most popular grips used today. ODI make the finest examples. If using normal grips fit them with some paint (put paint inside) and then when the paint dries it sticks the grips firmly to the bars, or you could try using zip ties.

Make sure flat pedals have got good Pin height left, if not replace the pins.

If using clipless SPD style pedals make sure your cleats are in good condition and that your pedals are clean and free or muck - you don't want to lose valuable seconds by not being able to clip in, or being repeatedly unclipped.

Make sure you use decent tyres and tubes when racing, and make sure you have enough tread for the conditions (especially if its muddy). If you can afford it buy a set of mud and a set of dry weather tyres.