I just want to add a little bit to that as well...
Common in the engine bay - Check along the fire wall - A lot of the MK1's and early MK2's seem to have holes in the fire wall
Also, with MK1's - out of the 5 I have owned, these are the common problems I've found after I've handed the money over:
1. Check the gearbox mounts
2. The floor - mainly the passangers side. My MK1 & Mk2 both had issues with the floor, one required having the whole floor pan replaced, MK1 someone had attempted to fix it had did more damage than actual repair.
A lot of these are common knowledge but can be forgotten in the hype so a basic run through:
1. Tyres - How much rubber is left and what size are the rims- rims (A MK2/MK3 are stock 14" and in most states its only legal to go 2" oversize so if they are 17" they might cause you issues with roadworthy, MK1's are stock 13") With below 50% you can use as a possible price reducer
2. MAKE SURE YOU TEST DRIVE. Check brakes, clutch has been covered in gards notes, as has gearbox. Just keep in mind 2nd Gear is the worst for a GTi, 99% of the time its the first to go...
3. Tint - is the tint of legal colour (not to dark), mirror tints & shadow tints are illegal in some states
4. Check that all the lights work in the car - tail lights, headlights, fog lights, brake lights, reverse lights & indicators. As much as it "might" just be a fuse or bulb, it could be something more costly as well....
5. Modifications: If it has had mods, has it been engineered? If it hasn't, have it checked by someone to make sure the modifcation will actually pass. Even a pod filter requires engineering in most states, so exercise caution
6. Ring REVS and have the car checked to make sure its clear of finance or you'll be left out of pocket with no car if the collecters come knocking.
7. Engine bay - Check for signs of oil - where its leaking from and how much. Leakage usually isn't a good sign.
8. KM's... A lot of people get totally *&%$%# with this. As your driving or even whilst the car is stationary, check to make sure the numbers line up on the odometor. If its sitting off, this usually means its been tampered with. Whilst you might think your buying a swift with 100,000km's on it, its really done 400,000....
9. Rust. Do a quick visual scan around the car for signs of rust - around the windscreen front/rear, and places the paint has bubbled. If it has a sunroof, check around the seals. MK1's - check around the boot hinges and around the tail lights as its a common bad spot for them. Don't forget to check the floor!
10. Exhaust - Whilst a totally fat sounding swift is awsome

most of the time its illegal. 90dB is the legal across most states, so if it sounds loud, it probably over legal.
11. As Snapper said about the timing belt - In theory this is supposed to be replaced every 100,000 km's with the pully done every 200,000km's. Usually a sticker will be in the engine bay on the cover to say when it was done, if in doubt just ask the owner.
12. Steering Wheel - If there is an aftermarket steering wheel, make sure that it is a full circle (even if it does have flat bottoms, it can't have no top and or bottom) and that its over 300mm or above in width.
13. Take magnets with you when you go to inspect the car. If it looks like it has been repaired in places, or you in general just want to sus it out, a lot of people are so lazy they just bog things up. Put the magnet on the car, if it doesn't stick, its been bogged in that place. That said, A lot of people now use metal shavings in bog so this is a bit of a hit & miss thing, but usually proper body repairers use metal shaved bog in prep...
14. Doors on MK2/MK3's are quite flimsy. Check where the frame of the window meets the door to for cracking (pull the rubber seal back as well) and also that the top of the door aligns with the roof.
15. Height - 100mm is legal height most states, so if it looks low...
16. Body Kits - I love swifts kitted up, they look tottaly fat

but ask yourself is it practical for where your going to be driving. I live where there a holes so big in the road they would swallow my swift whole, so living in suburbia might be fine to have a huge kit, living out in sticks means you'll find a fantastic friend in Tokyo race tape or you'll just destroy a front bar a week.
Thats my little add on

And Happy Swifting
