(If you need to pay a fine, by the way, and are having problems doing it online, this is a quick and fairly hassle-free way to do it.)
I started chatting to the ladies in front of me, and told them about the fine.
"Ooh, you've got to be careful," one said. "Last time we were here the guys who wash the car said the police had come and booked every car which didn't have their wheels straight."
I was 90% sure this was rubbish, and the car washers had either been winding up the ladies or there had been a major failure of communication.
But I decided to ask some Qataris what they thought.
"Most police won't bother you," said Ahmed. "But you know, there are some crazy cops. If you don't park your car straight they will come and book you."
"Whaaat," said his friend, who was a copper. "That's not true. It doesn't happen like that."
The conversation quickly moved into rather lively Arabic - I suspect Ahmed may have been booked recently and was still feeling sore about it.
I remain sceptical about whether you would get a parking fine for not parking straight. But at QAR500 a pop, I'm not going to take any chances.