After Samuel has his ear pierced, he goes to a party with his friend. When he sits with the cat on his lap, the earring repeatedly switches ears between shots.
In the scene at the fireplace, the hand that puts the tonearm onto the record is not Julianne Moore's, at least not the one that she is running through his hair.
While trying to operate the adjustable examination table during his first meeting with Sam and Rebecca, Dr. Kosevich knocks off the paper covering the table. It then reappears later in the scene.
While in the hospital, Julianne Moore's hair changes from behind her ear to covering her ear in between shots.
When Sam and Sean are talking after their tennis lesson, (just before Sam realizes he's late for the doctor), Sam's hair changes between shots.
When Rebecca is to be given an epidural, the doctor walks in with a huge needle. Epidurals are not administered that way. It is a procedure that takes at least 10-15 minutes.
When Samuel is driving his Porsche very fast, his hair isn't blowing in the wind at all.
When they are toy shopping, Gail calls Rebecca 'Missy' twice. But this may not necessarily be a goof, as "Missy" may just be a nickname Gail has for her.
When Samuel visits Rebecca in the hospital, there is no visible fetal heart rate being documented on the strip. The only lines shown are from Rebecca moving in bed.
Samuel is a child psychotherapist and yet he seems surprised by the Dwyer kids' idiosyncrasies and boisterous behavior. His interactions with them suggest he has absolutely no idea how to respond to them.