Bug: A game-breaking glitch can commonly occur during the prologue, upon creating a second character. *Spoiler* After the cryogenic chamber cutscene, after being released from the chamber, you will be stuck, unable to move or use any control except for Pause. The only known fix is to turn the entire game off and then go through the cutscene again.
Audio problem: During the prologue, when Kellogg shoots your spouse in front of you, you hear a shell-casing clinking on the floor. But Kellogg is using a revolver, which does not eject shell-casings automatically.
Other mistake: The character of Roger Warwick, or at least the one the player meets during the game, is confirmed by dialogue and terminal entries from the Institute, his farm, and Roger himself, to be a Synth. But killing him and looting his corpse will not reveal a Synth Component, as it will for every other Synth in the game, including ones like Deacon that the player is never supposed to be able to kill.