I too have had the problem with the "2 questions" being failed, strange it was the exact same number as yours as well  Anyway, mine was administered by the City of Richardson Texas when I was applying for a Public Safety Dispatcher. Mind you at this point I had been working for the City of Longview for 2 1/2 years as a dispatcher. Right off the detective made it personally known he did not like me  I can attribute this to our first encounter that was over a mischeduled interview date, entirely his secretaries fault. He then went over all documents I had provided and all forms I had filled out. I answered everything to the best of my knowledge in a way I felt was completely honest, yet he wanted to pull "technicalities" out on me. Such as a question pertaining to my driving record. I admitted to have 3 citations, speeding. One of which was me hitting a state sign while on duty during a rainstorm, but the officer wrote it as "failure to control speed" instead of an actual accident. So since it's on my record as "failure to control speed", I didn't mention the accident portion of it. Well, this ticked the detective off obviously 'cause he soon started in on me with "you seem to want to interpret these question how you see fit!". Needless to say I've come to the conclusion he was a complete prick, but anyway, back on topic  After this berrage of questioning, I was directed to take the polygraph by an outside agency. I had been through this before mind you, since I was working for Longview PD at the time, so I knew all 'bout "killing the snakes in the grass". Well, this particular examiner went into such shocking detail I did feel as though I was being interrogated! MY GOD! The things he would ask me, and then probe further, and further, and further, and FURTHER still!! Went on to even ask me about sexual activities as a minor WITH other minors. Now what relevance does THAT have??? Nothing illegal at all, geez. So needless to say, the polygraph did complete with no blows exchanged  But the examiner informed me I had missed "2 questions" . . . yeah, 2. So what does that mean?? Apparently it means you fail and I'll get to that in a moment. He told me it was regarding "employer theft" and "marijuana use". Now, we had already gone about with the employer theft. The ONLY thing that comes close is that I snagged a couple of shrimp and misc items from a restaurant I worked at when they were sitting out to be served. He advised me that this was not the type of theft he was concerned with, so that I should answer "no" on the exam. So I felt relieved. And the marijuana use . . . I told him all about my wild and crazy days in high school (class of 2000, w00t!!) and experimentation with marijuana. Fine right? Apparently not. So now that I failed 2 questions that I can't possibly fathom why come, I am pulling out my hair over EVER applying for another government agency again!!!  I had recieved a letter in the mail a week after that polygraph from Richardson stating somethin' along the lines of "Your application for employment has been disqualified. The reasons for our decision cannot be disclosed due to departmental policy". Well great  So I'm not accepted and they can't tell me WHY!?! Was it 'cause that detective had a bad impression of me??? Was it his personal bias??? Was it that damned polygraph with all 2 questions failed??? WHAT WAS IT!?! I am midway through the hiring process with another agency now, and next (I FEAR) is the polygraph. I'm a decent guy who is proficient at the job he's applying for. Now tell me if my fear is irrational 

~Deep~

I received official notice that I did, in fact, fail the polygraph examination with LAPD. I am more than disappointed as I know I did not lie on any relevant questions.

At any rate, I have already sent letters of appeal to two different people at Personnel, as well as having left a voice mail for my case manager. 

As I was nervous during the exam to the point of nausea and cold sweats, I am hopeful that they will see fit to give me a re-test as soon as possible.

The worst part is thinking that I will have this problem with every other PD I have applied to.