When Kono steps out of the grave that she and Chin just finished digging, in the first shot she is stepping out with her left leg. In the next shot she is stepping out with her right leg.
During Lou's search of his old partner's place, he finds a wall safe. When he looks at it, the door is clearly unlocked and he pushes it closed with his thumb before entering two sets of combinations - the last one being "correct".
The area of Chicago that Lou's former friend lives in looks nothing like what they show. It is much more urban then what they show, and more vintage buildings that tend to be built with brick. Chicago proper which is where they said (Hyde Park) does not have that much space between houses. What is shown is much more common of what you would see in the suburban areas that surround Chicago.
Grover committed several criminal acts in this story (assault, kidnapping, vandalism, among others) It has never been explained how he avoided prosecution and/or not stripped of his badge.
When 5-0 are getting out of the water and drying off. Danny puts on his shirt, and combs his hair. Next shot has him still drying his hair, but his shirt is buttoned.