Anyone who's been on the Resident Evil Facebook page for more than six months will know that Resident Evil 6 is hated by True Fans for everything. Literally everything. One of the arguments which confused me the most is that the Resident Evil 6 zombies are a mockery to the franchise and to George A. Romero due to their running and use of weapons. I'll handle these two separately, along with intelligence.
Now, George A. Romero's 1968 film is uncopyrighted due to an accident he and his team made, so for your benefit here is the movie itself (I'll give you timestamps when appropriate); screenshots will be the colour versions so you can see better. Here's the colour if you really hate black-and-white. Same timestamps.
You probably see zombies as having rotten legs or leg muscles, thus preventing them from walking properly; or maybe their nervous system is chaotic and the jerky shambling is the best they can do. Either way, the 'zombie walk' is well known as being the 'default' depiction of a Zombie.
In this scene (16:07), a Zombie smashes a car's headlight. It actually picks up a rock and smashes the light; the other zombie does the same.
In this scene (1:24:48), Karen Cooper (played by Kyra Schon) has transformed into a Zombie as the zombies outside finally break in. Confronting her terrified mother, Helen (Marilyn Eastman). When Helen falls over, Karen turns her attention away to a set of tools. Karen picks up a trowel and stabs Helen repeatedly in the chest.
We first understand their intelligence at the "Zombie smashing headlights" scene. It's not just angry - it's turning the lights off so it's harder for the zombie horde to be seen.
We see more intelligence in Day of the Dead (1985). One of the plots in this film is Dr. Matthew Logan's attempt to teach a zombie a number of things in the hopes he can eventually teach them social skills so they can re-enter society. It's also the Dr. Isaacs subplot from Resident Evil: Extinction (2007). In one scene, Dr. Logan shows his research to Captain Rhodes. When Bub - a former soldier - notices the Captain, he instinctively salutes. When Rhodes refuses, he growls in annoyance; Logan offers a salute instead and he calms down.
Logan gives him a handgun - unloaded - as part of another test. He feels the handgun and then remembers how to fire it. Bub actually mutters "reshee" (Let's See) and points the handgun at Rhodes (here's a clip of the scene). When it fails to fire, he checks the gun to see if it is broken. Either realising it is unloaded or just knowing it won't fire, he discards it.