Plot hole: The Death Note that Misa brings to L headquarters is supposed to be fake, but when Light touches it he can see the Shinigami Ryuk.
Suggested correction: Light saw Ryuk after he tried writing a name down in the piece of the notebook hidden in his watch. Since he touched that piece, it makes perfect sense he would see Ryuk as that piece was originally part of Ryuk's death note and wasn't swapped by L.
Plot hole: The Louvre is home to art worth millions. Even with the electronic security measures in place the museum would be guarded around the clock by armed guards thus making the entire idea of the shooting of its curator and his killer escaping impossible.