In the film version, I couldn't understand how two people (Dan & Alice) could live together for two years and stick to their lies. It seems to me the main plot is about Dan's cheating lies, and most people who see this play would think he's the only liar in the story. Consider that his relationship with Alice was strictly platonic and when Ruth, his girlfriend, found out that Alice was staying with him, she dumped him.
Most folks would think that Dan and Alice were actually sexually active, especially since she is a stripper. However, the only indication I ever saw in the film and the play was a kiss. I don't know why I am stuck on the idea that Dan doesn't sleep with Alice. Perhaps it is reluctance to believe that he could go two years without learning that her real name is Jane.
Isn't it possible the anonymous husband Anna is seperated from could be Dan? How does this idea affect the plot? It affects it about as much as Alice and Dan not sleeping together. It may explain Alice's defensiveness towards Anna during their first meet. Perhaps Alice knows about Anna, but Anna doesn't know about Alice, other than what she's read in Dan's book. I won't spoil the story for you by commenting on the ending, but just know this is they way I see the story unfold each and every time I watch it.