Ok, I think enough people had had a go. Zatharas got it right away - it was #3.
1 - I once uncovered a case of fraud in an Israeli military prison.
This one is a bit deceptively phrased - it's not quite as awesome as it sounds. As my compulsory military service, I served in the computer department of the IDF Military Police. Most of my role involved writing database queries, but I had other roles. At some point, once I was senior enough and had been promoted to sergeant, I occasionally performed computer inspections in MP bases, including the prisons.
In this particular occasion, I arrived at the prison and started inspecting the computers, when one of the local officers asked me why my department hasn't yet installed the computer that is supposed to keep track of family visits to the prisoners. As far as I knew, it should be running, so I went to see what was happening. Indeed, the computer wasn't working. As in, it didn't even turn on. After a few minutes, I determined the problem - it wasn't a computer, it was an empty case. Apparently, somewhere along the line someone had broken the computer case open (it was locked), took out all the electronics, and replaced the lock, then told the officers that the computer wasn't running properly. A criminal investigation was apparently started, but I was not involved in that.
2- I failed a driving test because I was driving with my eyes closed.
True. I have bright eyes and am very easily blinded by glare and that day was cloudy, so I didn't bring my sunglasses. The clouds cleared before my test, and I was blinded by the sun, and closed my eyes while continuing to drive. The examiner didn't appreciate that.
3 - I am double-jointed, and I can bend my fingers backwards so that they touch the back of my hand.
As Listener guessed, this is really a half-truth. I am double-jointed, and when I was growing up I was able to bend (some of) my fingers that far back. But I lost that ability in my teens - I can still bend them quite far back, but not to that degree. As a side note, I learnt the hard way that I am also capable of dislocating my elbows in a way that would be impossible for most people, though the one time I did it I broke the elbow while trying to re-set it, so I'm not going to try that again anytime soon.
4 - Once, a taxi I was riding was stopped by the police. It turned out that the driver was an escaped felon who had stolen the vehicle, then proceeded to drive it as usual.
Entirely true. I was 8 years old, and my parents and I were living in Boston for a few months while my father was teaching there for a semester. My grandparents came to visit us, and we went to the airport to pick them up, then took a taxi back, which was followed by police sirens and the driver being taken away in handcuffs. I remember standing at the side of the road waiting for a replacement cab to arrive. At the time I was mostly confused, but my parents have told me the details later.