When the surviving partner enters the crime scene he does not have an injury on his hand, then he is asked what happened to his hand and a covered injury shows on the palm of his hand
To this day, the Empire State Building has window washer cleats on its windows, all of which are double hung and open from the inside for the window washer to gain access to the outside of each window. The "building" being climbed by victim #1 had no cleats and no way for the window to be opened.
When the surviving partner first meets Mac, Mac has just removed his right glove and is about to remove the left one. Yet as the partner leaves you hear Mac remove 2 gloves.
When Mac traps the mosquito under the jar, he describes it as being "fat and well fed", yet the close-up view of the insect shows that it is not, in fact, engorged and, therefore, not fed.