Dr. Karev's board results letter lists his title as MD, FACS (Fellow of the American College of Surgeons). He is still an intern and therefore cannot be a Fellow.
Someone wrote that the letter from the Medical Examiners National Board was written to Alex Kaver, MD, FACS. The letter was addressed to Richard Webber, MS, FACS, Chief of Surgery, NOT Alex. The letter was about Alex. It is at the 13:55 mark on Hulu.
When Bailey is getting into the elevator to go home, she says she has been pregnant for 47 months, instead of weeks. Since the average length of a pregnancy is 40 weeks, this was most likely written deliberately to evoke a sense of exaggeration.
After Meredith discovers Derek visiting her mother at the nursing home, when it cuts to Miranda in the OR the T-mark can be seen on the floor at Cristina's feet.