In the shot where Mr. Richards, Bruce, and Dennis hear a rustling noise, Dennis can be seen sitting down without his tomahawk. In the next shot though, you can clearly see the tomahawk resting on his leg.
On the quick shot of the paper titled "The Plan", many of the writing is in Russian, although there are still words plainly in English, including "The Plan", "America", "President", "You", "and "Mullet". Having these in English would not make much sense.
In the shot of the explosion on the hill, you can faintly see a line below the explosion, as if the explosion itself is floating.
Mr. President refers to the hills as "the Northern Hills" and the "hills north of here". Although the film is set in San Francisco, the actual hills are in Las Trampas Regional Wilderness, which is east of San Francisco.