Continuity mistake: The amount of beer in Clinton's (and in Greta's) glass fluctuates. For example, Clinton's glass is almost full, but is even closer to the rim the second time it is shown. After the amount decreases (even though he isn't shown drinking any), the amount in his glass is fuller again. (00:45:20)
Other mistake: The grave that Clinton dug for "Mouser" was not even close to the recommended minimum depth of 3'. After placing the box in the hole, the cat's remains would have been within about a foot of ground level, which was close enough for the cat's scent to attract animals which might/will dig up the grave. The roots of Mouser's favorite tree should have interfered with the ability of Clinton to dig there without obstructions. Also, some states or local ordinances prohibit backyard burials of pets. (00:24:28)
Revealing mistake: When the newscaster was filming Clinton giving a statement, the timer on the camera stayed at 0:00. The red "Rec" button, which supposedly was on, also looked fake. (00:10:35)