I'm glad I've found this!
We're not assuming that the people who put the bomb in his car had his own set of keys, are we? It would have been planned since the death of the VP a few days before - whoever planted the bomb knew Brody would be going to the memorial. It's relatively easy to get keys for any car.
I think there's more to Saul than meets the eye. There's more to Quinn than meets the eye, too. Why didn't he kill Brody in the woods? He saw him praying - has Quinn spent time in Iraq too? Is he meant to be Moslem, too?
I notice Brody doesn't abide by any other Moslem rules - he eats whatever he wants and he drinks alcohol. Having a prayer mat doesn't make you religious, Brody!
I thought it was very odd that they both stepped away from the service. Surely that would be noticed, particularly as Brody was the VP's running mate? It would be seen as very disrespectful. It would have made more sense if they'd stepped away from a party afterwards.
One thing nobody's mentioned here though is that they could have both been tracked by their phones. It's hard to believe Carrie's car wasn't tracked, too. If their phones were tracked, it could be seen they were together.
Did anyone else notice that Carrie just said "Oh go up there, the hut/house is about 20 miles away" and pointed Brody in the direction of a pitch black field? He didn't seem bothered by this, either!