do Europeans regularly have problems passing the exam?

The particulars of the exam will vary from country to country, but Belgium supposedly has one of the more lax ones and even here you routinely hear of people failing their driving exam. I actually looked it up because of your question and according to wikipedia:

• About 47% of the written (theoretical) exams are successes. It's hard to say how many people fail, since you can try several times (and fail all of them).
• Around 56% of the road tests are successful. Again, people can take multiple tests per year if they fail (although this is limited somewhat in that you need to spend time and money after failing every second attempt).