Continuity mistake: During the sex / assault scene, the President removes her shoes. After being shot, her shoes are back on her feet.
Other mistake: When Luther is driving the Senator to the White House it is raining. But there is a shot of Luther from the outside front window and the window is perfectly dry even though side and rear windows show that it's still raining.
Plot hole: When Luther places the envelope on the table during the White House tour, he is not wearing gloves, thereby leaving his fingerprints behind.
Answer: The female detective states the carpet is spotlessly clean, indicating they had performed an intense cleanup not shown on camera so they would no doubt cover the staircase as well and wipe it clean of prints. As for the crowbar, it is more than likely part of a "kit" in the boot (trunk) of secret service vehicles.
The_Iceman