In the beginning when Adonis is typing his letter of resignation he is wearing a black tie. When he turns his resignation into his boss his tie is blue. When he goes home and Mary Anne asks him how his new job is he is wearing the black tie again.
Towards the end of the movie. After Adonis Johnson (Creed) shows up at Bianca's apartment door, the top dead bolt is already in the unlocked position (north to south). Adonis and Bianca continue to dialogue and the dead bolt remains in the same position. Yet just before Bianca finally let's Adonis in, the dead bolt is suddenly in the locked position (east to west) and Bianca ends up unlocking it (north to south) to let him in.
After leaving the dressing room to enter the arena at Goodison Park, Merseyside, England, an American exit sign with red text can be seen above the door. UK exit signs are green with a pictorial of a man and a door. This was clearly not shot it the UK.
When Adonis is at the Delphi gym, which is supposed to be in Los Angeles, you can see a Pathmark behind Adonis on the other side of the street. Pathmark was supermarket chain exclusive to the north east.
The goof item below may give away important plot points.
At the end of the movie, Adonis and Rocky visit the Museum of Art. Adonis looks around as if he hasn't been there before, and says, "This is it?" However, Adonis was there when first came to Philadelphia, as he visited the Rocky statue which is located just off to the side of the famous steps.