While Ducky is in his living room his bow tie changes from proper placement to sagging back to proper placement.
The sailor comes out of the building towing a suitcase but after he kisses his girlfriend the shot widens and the suitcase is gone.
Prior to the attack on Ducky, the knife blade is fully covered with blood. After the attack, when we see the knife in Ducky's hand, it is mostly clean.
People are wearing coats and the cold is explicitly commented on. But the trees outside the office window and over the victim's body are in full leaf, which would be impossible in winter in the Washington DC area.
When McGee is unpacking his old computers, he identifies the first computer he pulls out as his first computer as a Mac SE, yet the actual computer he unpacks is clearly a Macintosh Classic according to its label.
As David McCallum as Ducky puts an LP on the turntable and tries to fascinate with his knowledge of the Afghan history and culture, he can't even pronounce "mujahideen" correctly, mumbling something like "muhahadeen" instead.