When Renzo walks to Megan's table to tell her about his "special talent" he is wearing his suit coat. The scene then cuts to the group watching him walk over. When it cuts back to Renzo he is not wearing his suit coat.
After Teddy has his encounter with the wedding cake, he takes off his jacket and starts to leave the room. When he does, the third button down on his tuxedo shirt is undone. A few seconds later as he is walking out to leave, he turns and the button is now buttoned properly, yet Teddy never took the time to button it back up.
When Eloise is talking to Teddy, alone in their first argument about him being "a ridiculous father" (as he interpreted her point of view which caused the break-up), he has a string of his hair hanging on this forehead. Every so often there is another take where he doesn't have it hanging on his forehead, after they switch back and forth from Eloise, back to Teddy.
The goof item below may give away important plot points.
A major subplot concerns Eloise eating an abundance of hot dog minis and vomiting, which tips Nanny Jo off to El's secret pregnancy. The modern-day pregnant woman is explicitly told not to eat hog dogs, fish, etc. during their pregnancy, especially in the second or third trimesters. Considering El was planning on keeping the baby (with or without the father's support), she should have kept away from the hot dogs to begin with.