I am a big fan of used German cars. I have has a 1998 Audi A8, 1990 Mercedes 560 SEC, 2006 VW GTI and a 2008 Audi A8L. I have also had a Volvo 940 and a 760 Turbo station wagon. I still have the GTI and the 2008 A8L. I disagree that owning a nice German car is all about status. That is like saying that a person who buys a Wilson Combat 1911 or other high end pistol is only about "status". That is simply not the case IMHO. There are performance and yes luxury reasons for purchasing these types of cars.
First if you are looking at a particular model look for a forum for that car make. Look on that forum for the sub-section for your car of interest and its generation sub forum. Most of the time they have a buyers guide which will list all of the common failure points on a particular model. For example on an D3 Audi A8L you need look at the air suspension, upper control arms, truck motor, air bag sensors, parking break etc... Know where the problem spots are going in. If they have not been addresses chances are you will be addressing them at some point.
The way I buy them is to look for a single owner car that was leased or purchase and driven for 3-5 years. Look for cars which are 1 owner lease for 3 years then purchased by the same owner under a CPO program. If I am looking for a VW I search Audi dealers. If I am looking for a Audi I look at Porsche, Maseratti and super high end car dealers. They often get the most cherry trade ins because the people trading in there are stepping up to $100K cars and if they can afford the 100K car they did the maintenance on the last one often at the dealer. The problem with a lot of the used German cars in the market are that people do not understand how much the regular maintenance will be on these cars. Oil change are not $24.99 specials they are $50 to $300 depending on the model. In the early stages of ownership warranty mandates dealer service so cars still under warranty are the best bets. CPO are the next best bet.
Make sure that the car was dealer serviced if at all possible. You can pull a Carfax and see dealer service. Typically the leased cars are best because they are serviced at the dealer. Then get the Vin and call the dealer listed on the Carfax. Tell them you are looking to purchase said car and then ask for the service records. Some dealers will give them to you other will not. If they won't then at least ask the service writer to look and it over and see if there are any odd repairs or things out of the ordinary. Ask about the trouble spots. Have they had issues? Most of the time you can get the info you need. From there you can assess the car's current condition vs what it might need.
Those who pointed out the electrical issues with German cars are 100% spot on. That diesel engine will last for 300K but the windows won't work, every dash warning light on the car will be on, your keyless entry might not work, you seats won't move etc... The German cars are a bit over engineered at times and those electrical things go long before the engine itself goes. With a 2003 I think you are pushing it a bit because it has most likely had more than 1 owner. It most likely has not been dealer serviced for a long time and most likely has no records. My advice would be to take it to a local indy mechanic who specializes in BMWs and have the look it over. Buying one of these cars without and good inspection is a huge gamble. If you are not going to do the work yourself, because there will be work, make sure you have a good local indy mechanic. They will save your ass vs the dealer. I like ones that will use parts you source from people like ECS Tuning in Oh. They have a great mix of proven aftermarket parts and factory parts for German cars.
Even if you are not going to do the work yourself invest in a good scanner specific to the brand. For VW an Audi I use a Vagcom which will allow you to read all the codes. Reset lights and do diagnostics just like the dealer. I don't do my own work but by having the Vagcom I can turn off intermittent gremlins that pop up. As the car ages those lights will pop on. If you have the right scanner you run the scanner and then post the code on a BMW board and people will tell you if it is minor and can simply be reset or it needs to be addresses. As they age more and more of the issues that cause the lights to come on are electrical issues and are not serious but intermittent annoyances. Also anytime I bring it into the shop I know what system is failing.
At about 12-15 years of age is when I dump them. The cost of maintenance starts to outweigh the value of the car and I basically rinse and repeat the process. This car is right on that line and I would be weary unless you can get rock solid documentation on service. As for the warranty it is only as good as the company underwriting it. I have had mixed results with them. Even a good one is a gamble. It is betting something is going to fail. I have done it in the past but these days I take the $$$$ that I would have paid for the warranty and put it in a savings account for the car and basically self finance a warranty myself.
To me this car is a risk unless you have $1,500 to $2,000 cash to address any issues that come up. A minor issue can easily become a $1,000 repair. With German cars my experience is to pay for the best condition car you can upfront because if you don't you end up paying more on the back end.