Apart from what the above has been mentioned:
1. Vacuum pipes must be checked, you probably stepping into the PWG on the 135i so vacuum leaks can be a PITA.
2. Turbo inlet pipe and intercooler pipes, inspect and replace with upgraded ones too, also known to get leaks.
3. Check the HVAC system, many of the BMWs end up with leaking ones which leak into the interior and end up getting the car smelly. (most older BMWs have this issue but I found many have happened on the x35s for some reason).
4. If the car does get tuned or has a tune, don't get 2-step colder plugs... get 1-step colder unless you going over Stage 2 or higher.
5. Get the sump gasket looked at as well, they are common too so if you going through all the other oil leaks then get to the sump as well one time as it is relatively cheap to fix. gasket was R1200 with bolts (a ton of them needed).
6. If you do replace the DV, and you decide on GFB...get the original GFB. There are a ton of fakes doing their rounds, and its a PITA to fit them and the cheaper ones don't last long but the GFB also makes a nice sound.
7. I didn't have issues with my waterpump thankfully but it gave yup shortly after the new owner got it, so even though it seems fine...just buy one in case because it pops up at the worst of times. Handy to have replacement available rather.
8. Check the turbo seals on the car when you get it and check the oil sweats around the turbo. Also check the actuator arm if there is any play as well.
9. Check for any residue on the rear axle and diff to see if the car has been spun before, then you know what strain was placed on it before.
10. Consider fitting a oil-catch can for excess blow-off.
11. Gearbox service dependent on mileage and type of gearbox you buying. The service made a world of difference.
12. If manual, check the clutch out...they a bit pricey to replace and if the car was spun before...that might again give you an idea of maintenance expectations.
13. Didn't get carbon clean done but many that have done it on N55, say it really does make a good difference.
14. I didn't have any issues on coilpacks but many have caught out a few coils on lumpy idle, can also check this in advance too.
15. Many will tell you to also upgrade intercooler but if not tuning and even up till Stage 2, Intercooler is optional. I fitted a bigger one anyway due to getting it for a good price and it helped when hooning the car but for daily drive and things, the stock one was still fine. However, the intercooler getting a good clean helps, they get a lot of rubbish on it and only when you take it...you realize how much it has accumulated.
16. I upgraded the filter to a flat pan K&N, the intakes on N55 unless closed have not been favorable (few threads of owners here experiencing that. The upgraded, drop-in filter was excellent and to clean etc is better.
17. Keep oil change intervals between 7500 - 10 000km, can go the 15000km but 10000km is like the sweet spot.
18. xHP gearbox tune is also pretty lekker, gives the gearbox a whole new feel all round and money well spent.
19. Injectors - Can get them cleaned up as well one time if you do a carbon clean, many N55 guys have complained off failed injectors and best if you get them tested ahead because they also can cost a packet to replace.
20. Check the OBD plug and check if it is really lose, tell-tale sign that the car was being logged a lot and possibly tuned before.
21. And then there is also the vanos issues (Solenoids, seals etc.)...prep yourself for these. Limp mode, Engine light or sluggish ... this is also a kak job too.
22. VVT motor as well, that goes with the Vanos...can be frustrating once it gives you issues and to diagnose them.
These are top of my head from ownership and experience through the time I had my N55, granted mine was good and didn't give me many issues but I kept my eye on these things while I had it as well.
