Continuity mistake: When Ana and Christian are having sex on the dining room table, she drops Christian's pants below his butt. Scene cuts and Christian's back is shown, with his pants above his butt. Then cuts back and they're below again. (00:54:40 - 00:56:50)
Character mistake: When Anastasia has to make out the 5 million dollar check to "cash" to get the money to release Mia, she signs the check with her old last name, "Anastasia Steele" instead of "Anastasia Grey", which is written on the top left corner of the check.
Suggested correction: A key point in the movie is how Christian is upset that she didn't take his name in her work life, so it wouldn't be unreasonable that she signed the check using her maiden name (it also could have been just as easily a force of habit thing, it does take time to get used to using the correct name!).
Continuity mistake: When Jack calls Ana from Mia's phone, he makes his demands and throws Mia's phone in the water. Then from the bank Ana calls Jack on a cell phone.
Other mistake: During the Honeymoon Montage at the beginning of the film, there's one moment where Christian and Ana are on The Fair Lady boat and Ana's wearing a spaghetti strap shirt/dress and Christian's wearing a blue denim shirt. This would if not later on in the movie we see Ana slipping on this shirt and Christian in the blue denim shirt, AFTER the montage scene even though it hasn't happened yet. This is even more evident by a deleted scene - The Hickey/Apology Scene - which takes place just before Ros called to tell Christian and Ana about the fire at GEH. So, basically, they wore these clothes before it was actually shown in the movie.
Continuity mistake: When Anna is lying on the concrete and you hear Christian say, "Anna, breathe," she disappears while cops are arresting Jack.