Rod Ends
Rod ends can almost be looked at as wear items, like brakes or tires. Although brakes and tires wear out at a much quicker rate, rod ends directly transfer high loads, and take tons of abuse on a regular basis. Add a dirty, unfriendly environment to the mix, and the rate at which performance degrades increases. All of your rod ends should be cleaned and greased on a regular basis. While cleaning, you should check for smooth operation with no wear. Check for cracks in female ends and bent male ends, clearance and excessive wear, and cracks in aluminum ends (your not really using aluminum rod ends are you?)
Brakes
Braking systems see a ton of torture to say the least. In short-track racing, brakes see the most heat and abuse of all the systems in most race cars. Besides brake pads, which wear over time, heat can damage piston seals causing leaks, and cooked fluid, which reduces performance. Inspecting for issues before they become serious problems is huge--the last thing anyone wants is to drive into a corner and find out they have no brakes. A thorough inspection includes checking seals, pads, fluid, and caliper alignment. Brake fluid should be replaced fairly often, as moisture build up is common, and excessive heat for long periods of time breaks fluid down. Rotors and calipers should be checked thoroughly also. Check rotors for deep cracks, excessive wear, and warping. Improper caliper alignment can cause damage to the caliper, and if damage is present, said caliper should be replaced.
Steering System
Any time there are moving parts, wear can be an issue, and there are a lot of moving parts in a race car's steering system. It is very important to inspect these moving parts (steering box, tie rods, drag link, idler arm, spindles, or rack-and-pinion if your car runs this style of steering), as almost any damage can decrease steering ability. Check for slop. Loose steering can be a good sign that something in the system isn't right. Check the seals for leaks, idler arm bushings on drag link systems for wear, and look for bent drag link components. Once everything is checked and reassembled, run the steering through its entire range of motion. Look and feel for any tight or dead spots, and ensure the steering is smooth through its entire range of motion in both directions.
Rearend
The driving force of your race car is something that needs to be taken care of. The rearend sees many different forces as a car goes around the track. Engine torque is transferred to the rear wheel through the rearend, loads are shifted to the chassis through the rearend, and the weight of the car sits (literally) on top of it. Many times in wheel to wheel racing, the rearend can be damaged, and it may be minor enough that there is no visible damage, but over time, small amounts of damage can turn into big issues. When you have the opportunity to inspect the rearend of your race car, check the seals for any leaks, replace the gear oil, and check the axle tube to ensure nothing is bent. The internals are just as important. Check the pinion for play, check and/or replace springs in locker-type rearends, check the ring gear and pinion gear for wear, and look for bent or worn axles. Once your inspection is complete, check for worn lug nuts and studs (especially if your series has pit stops).
Springs
Check your springs for any height change from the start of the season. Although the tensile strength of the spring's material won't change, the height of the spring can change due to the constant weight of the car resting on it. This height change can affect the setup, as roll centers, corner weights, and ride height will all be affected. Beyond the height, check for bent springs and signs of coil binding, rubbing on shocks for coilovers, and incorrect mounts that contact additional coils on big springs. Note: Springs don't lose rate, they can lose height and that might increase the rate. The reduction of height with the same number of coils brings the coils closer together, which can add to the advertised spring rate.
Tying It Together
Preventative maintenance is important. The more time you spend examining the car and its components, the more familiar you'll be with it and the easier it'll be to spot problem. In most cases, small problems can turn into larger, more expensive ones, and catching them early can save you time and money, and many times will result in less part failures on track. Clean and inspect your car often, it's an important step on your way to the winner's circle!
Chassis
There's no denying your chassis has a rough life. This is why it's important to inspect it regularly. Hard racing, bumpy tracks, even being strapped down in the trailer can cause bends and stress cracks that might not be easy to find. This is why checking the welds at the pick up points is extremely important. Once you've inspected everything, string chassis and measure for any changes--especially if you've been involved in any wrecks. Do a complete chassis alignment with strings or lasers to ensure the front or rear clip has not moved. What may have seemed like a light hit can cause large amounts of damage.

Welds on the A-arms, as well...

Welds on the A-arms, as well as on the A-arm mounts should be checked for stress cracks. If the welds are cracked, they should be ground down and rewelded or junked and new ones purchased.

Brakes are very important,...

Brakes are very important, so they should be checked regularly. Measure the rotor thickness to ensure they are within manufacturer specifications.

Also check the rotors for...

Also check the rotors for cracks or warping. A cracked rotor can come apart causing a lot of damage in the process.

Check for proper caliper alignment....

Check for proper caliper alignment. A misaligned caliper can cause one pad to drag the rotor, which can cause brake issues and slow the car down.

Check the steering box for...

Check the steering box for leaks.

Check all of the links for...

Check all of the links for bends.

Check all joints for wear,...

Check all joints for wear, and make sure the system moves smoothly through its entire range of operation.

Inspect the cover, hardwear,...

Inspect the cover, hardwear, and gears. Quick gear changes can damage commonly used parts as they get thrown around in a rush.

Inspect all of the seals and...

Inspect all of the seals and bearings in the rearend. Leaks and worn bearings can cause bigger, more expensive problems.

Inspect the gears for excessive...

Inspect the gears for excessive wear. If the gears are worn, replace them.

Inspect your springs for wear....

Inspect your springs for wear. If you run a coilover setup, check for contact with the shock body or shaft. Ensure the springs sit correctly in the spring cup.

Measure the height of the...

Measure the height of the springs, as springs can lose height over time. Also, check the rate and adjust your setup accordingly.

Check the front and rear clip....

Check the front and rear clip. Clips can move as a result of even small wrecks. String the chassis to ensure all four wheels are pointed in the right direction.

String or a laser will give...

String or a laser will give as accurate, straight line to measure off of. For detailed information on how to string your car see the story by the same name in the April 2012 issue of Circle Track.