Other mistake: When Helen Mirren and Will Smith are standing on the subway platform and the scene cuts away to view them from the other side, we see them through the windows of a passing train. Dame Helen suddenly gets out of character and hastily answers her cell phone. She was playing a "spirit" on behalf of Will - not someone who'd have a phone. (01:04:00)
Continuity mistake: When Will Smith is being recorded by the private eye, she holds the cellphone vertically. Also, there's a lot of background noise -especially in the subway - yet when the video is played it is a horizontal video with perfect sound.
Answer: They did recognize each other (at one point he goes to her house without asking her address). After the divorce, Howard said that he wished they were strangers again. They literally behaved as if they never met each other before (even though Madeline is gently pushing to move past being strangers - for example, by guessing he's divorced).