Just before baby Emma is named in the hospital and Rachel starts crying, Monica is holding the baby under the back, not supporting the head at all. From the next angle, when all of the friends are visible, the whole body of the baby is supported even though Monica hadn't changed her grip.
When Rachel holds baby Emma for the first time before sharing a kiss with Ross her hair is tidy and behind her ear,during is messy and sweaty and then they go back being tidy again.
When Ross talks about Janice "contracting and everything", you see Chandler bring both hands to his face. In the next shot, one hand is at his chest and the other is by his side (2:53)
While in the recovery room when all the friends are holding Emma for the first time, there is a cabinet door behind Ross that starts out closed, then is open for awhile, and then is closed again until the end of the scene. None of the friends ever reach back as if to pull something out of it, nor is any hospital staff in the room at any point during this scene, as if they were doing some sort of medical task that required the cupboard to be open.
Ross started having feelings for Rachel when he was sixteen years old, not fifteen, as Phoebe states. In pleasant conversation, though, one doesn't always remember exact dates/times/ages, and will often "round up" or "round down" to estimate.
When Monica holds Emma for the first time, she says to Ross and Rachel, "I'm so glad you guys got drunk and had sex," possibly implying she was conceived during their trip to Las Vegas, which was an entire year prior. However, Ross and Rachel were also downing a bottle of wine together in 'TOW The Red Sweater' (actual impregnation date). Monica could easily be assuming that the shared bottle of wine made them both drunk, as everyone saw the wine in the videotape of them together.
In the final shot where Ross is walking from the elevator, it can be seen that at the far end of the corridor there is no ceiling, and studio lights are clearly visible.
When Phoebe and Ross are in the Nursery watching the nurse putting the baby in her bassinet, as Ross says "Look at Emma," the baby name tag on the bassinet is seen to read Geller-Greene, misspelling Rachel's last name.