When she called her butler for the car it was raining. He rushes outside to get the car and when she drives off, there's a distinct dry patch.
In the UK, police cordon tape used at crime scenes is blue and white not yellow.
Following the funeral, Elizabeth asks Robert why his uniform is different from the others. He responds that this is because they are in the British Army. As a US Marine, he would know that the guard of honour or honor guard (if you speak American) was comprised of Royal Marines, the Royal Navy's elite fighting force, and definitely not Army.