Carol talks to Jean-Luc about when her first husband divorced her, but in the First Season, it was clearly identified that Carol was widowed by her first husband.
When Carol steps over the fallen door at the salon, she has high heels on but when she goes to drag Jean-Luc out of the room, she has no shoes on. At no time in that scene did it show her taking off her shoes.
In this episode, Lily says she's 5 but Carol only gave birth to her 2 seasons ago. It would make more sense if they aged the rest of the kids the same amount of time but it would put JT at 22 when he is younger than Dana (who is 21 this season).
When T. Edwin Jarvis comes into the Beauty Salon and shows Carol his badge as he announces that he's from the White House, he holds up a badge that clearly shows a woman's picture on the badge.