This is long but is what I looked at when buying my beamer. Its designed for a E36, [ edit - for a E30 318is NOT E36 ],but ALOT of this goes for any beamer, or car in fact. Here goes:
What to look for when buying
If you are thinking of buying a 318is follow this list of suggested items to check. Many are obvious, but may save you time and trouble in the future. Hopefully it will help you to avoid the hacked cars out there, as most 318is will probably require some work given their age. I have listed a number against each to indicate the potential seriousness (=cost!) to help you gain an insight into the faults. 1= Serious fault 2=Of concern 3=Minor fault. Engine
Check for ticking noise coming from valvetrain, especially when hot (1)
Check for a noisy timing chain - a hissing noise esp. around 3-4,000 rpm (2 if slight, 1 if severe)
Check for a replaced BMW OEM profile gasket (1)
Check for a blown or blowing head gasket (1)
Check service history (preferably BMW but a well documented history is better than none) (2)
Check oil type used (synthetic is best, good brand second best) (2)
Check for smooth reving up to 6250rpm (1)
Check for blue oil smoke from exhaust on both cold startup and overrun (1)
Check for steady idle at ~850rpm, both hot and cold (2)
Check for water leaks (evidance of antifreeze around engine bay) (2)
Check for overheating (1-2)
Check condition of spark plug leads - they are expensive (2)
Check condition of vacuum hoses around inlet manifold (3)
Check for significant oil leaks from rocker cover (3), head gasket (1), timing covers(3) and oil pan (3).
Check for excessively noisy injectors (1)
Check for a ticking around the inlet manifolds (x2). Inspect for any signs of manifold cracking (2)
Check for failing exhaust maifold gaskets, detectable by a ticking when under load. (2)
Check for fuel leaks around injectors (2)
Check for a failing fuel pump. A hum should be noticeable from inside and outside the car but it should not be excessively noisy. You should not be able to hear over the cars' noise past ~40mph. (1)
Gearbox & Transmission
Check for a relatively smooth and short gearchange. Be aware than many 'boxes are notchy when cold. (1)
Check gear linkage for freeplay (2)
Check synchro in all gears (except reverse) (1)
Check history of oil change in gearbox and differential (ideally every year although ever 2 years is satisfactory) (2)
Check gearbox for excessive leaks. Slight weep from the rear is normal (2)
Check differential for leaks. Some weepage from the driveshaft sides is normal (2) but a pinion oil seal is more problematic (1)
Check guibo (flexible disc in the driveshaft) for cracking around the bolt holes (2)
Check both CV joints on both halfshafts for noise and damaged boots (2)
Check for vibration when driving. If the car vibrates from 5
60-80 mph/100-140 kph the driveshaft could be out of balance or the guibo worn (1)
Check for differential whine above 50mph (1)
Check for gearbox whine, especially if evident in all gears (1)
If mileage is over 120,000 miles/200,000 kms, enquire if the clutch has been replaced. If the car has done a lot of town driving it may be due (1)
Check for a very stiff clutch pedal (1)
Check for a very soft clutch pedal (2).....
.....Check clutch slave and master cylinders for evidence of leaks. They last about 10 years or 80,000 miles (2)
Brakes
Check for regularily changed brake fluid, DOT 4 or better (3)
Check for front and rear disc/pad wear (3)
Check for disc condition - scoring, cracking or pitting (2)
Check for damaged flexible hoses to calipers (2)
Check metal pipe around the back axle, especilally over the subframe (2)
Check for caliper failure/seizure (1)
Check if the car vibrates while braking the discs could be worn (2)
Check for damaged pad wear sensor at front left and rear right calipers (3)
Check for failing mastercylinder (with the engine running, press brake pedal firmly and watch for it to creep down) (1)
Look for leaking parts by checking brake lines, especially at the master cylinder, at each caliper, ABS pump and at each end of the flexible hoses (1)
Wheel and tyres
Check all wheels (don't forget the spare) for kerbing, damage and corrosion (1)
Check all wheels for bolts (3)
Check all wheels for centre caps (3)
Check all tyre for wear and evenness (2)
Check for the same tyres on each axle (3)
Check brand of wheels and tyres - it can give an indication of the care lavished (3)
Suspension
Check rear suspension subframe bushes for wear (listen for a clonk when acclerating hard in first and watch for a wandering during high speed turns) (1)
Check rear trailing arm bushes (1)
Check wheel bearings for noise or roughness (1)
Check rear damper upper mounts for noise (2)
Check all anti-roll (sway) bar bushings for cracking (2)
Check front contol arm (wishbone) and balljoints freeplay (2)
Check front control arm bush for cracking (2)
Check steering rack freeplay (1)
Check power steering pump for noise and leaks (1)
Check steering rack rubber gaiters for cracking and leaks (2)
Check inner and outer track rod ends for freeplay (2)
Check tyre wear pattern - a slight bias towards the centre of rears and inside of fronts is normal (2)
Check dampers (bounce and leaks) (2)
Check rear damper upper mounts for movement (3)
Check for a level car from behind (1-2)
Check for a level car from the side; note that the front sits lower (1-2)
Check front top strut mount for exesssive freeplay (1)
Check the car does not pull or wander (however bigger tyres may "tramline" over ridges and painted lines (2)
Check for vibration when driving. If the car vibrates from
50-70 mph/80-120 kph the front control arms, etc. could be worn (1)
Interior
Check seats for operation in all directions (1)
Check seat hinges and springing for wear (1)
Check seat frame (especially the backrests) for breaks (1)
Check condition of seats, carpets, gear knob and pedal rubbers - they should verify the cars mileage (2)
Check rear demister works (2)
Check air conditioning blows hot and cold when engine is fully warmed up (1)
Check that the wiper, indicator and light switches work (2)
Check windows for operation (2)
Check central locking for operation (2)
Check sunroof operation (1)
Check for operational instrument guages (2)
Enquire if SI board batteries have been changed in the last 5 years - they last between 5 and 10 years (2)
Check door cards for damage or wear (2)
Check screws around instrument cluster. If worn, enquire why - the car may have been clocked (1)
Check footwells in boot for evidance of damp or rust (2)
Check carpets for dampness (2).
Exterior
Check general headlight alignment (2)
Check headlights & lens for damage (3)
Check hydraulic headlight adjusters if fitted (2)
Check panels gaps are equal around the car (1)
Check bonnet fit (1)
Check for a straight line along the crease down the side of the car (1)
Check for an original front valance (1)
Inspect the front suspension turrets, jacking points and suspension mounting points for signs of rust (1)
Check for evidance of oversprayed paint under window seals, around lights, behind bumpers, behind radiator grill, on front valance/spoiler, exposed wiring looms, gutters, under door handles, etc. (2)
Previous Owner
Investigate the type of driving previously undertakem (urban or rural) (2)
Assess the care given to the car by the previous owner (2)
Assess what modifications (is any) have been made to the car and what their purpose was (2)
Assess the level of maintenance given (1)
Assess the attitude of the previous owner (1)
Check that all paperwork is correct and match chassis and engine codes to the log book. (1)
General Other Checks
Check for road tax expiry date - if it is a long time in arrears then the car may have been sitting idle / unsaleable - WHY?
Check road tax books for frequency of renewal.
Check chassis, engine numbers and body colour against documentation.
Check the toolbox, jack. brace (wheel spanner) and warning triangle for condition.
With a multimeter, check the battery voltage reads above ~12.2 volts. With the engine running this should rise above 13 volts.