Naomi says her grandfather was in the FBI, but later, when Master Miller mentions him, he says "her grandfather" and "her father". (this error was also present in the original Metal Gear Solid (1998).)
In the cutscene where Gray Fox slaughters the soldiers with his sword, he cuts one of them in half at the waist. After the cutscene, the player controls Snake to walk into the hallway in which the soldiers were killed, and the soldier that had been cut in half is no longer there.
When Gray Fox is defending Snake from Metal Gear REX, he impales the radome with his sword. While firing frantically at the radome, Fox's sword comes loose and lands at Snake's feet. As Fox is being crushed by REX, Snake runs over to his aid, leaving the sword where it is, and stays in his new position closer to REX. However, after Fox is killed, Snake looks down and the sword is still at his feet.
After talking to Meryl in the restroom Meryl says "that's strange there's no guard". Snake replies saying, "What's happened to the music?" but the music is still playing.