Lady: "You know, I think the problem we're having getting to the right alignment is because of the slip pivot."
Gentleman: "What slip pivot? There's no slip pivot."
Lady: "Yes, there is. But it isn't working well and we aren't getting around enough."
Gentleman: "There's no slip pivot in that figure."
Lady: "Yes there is. Watch." Lady demonstrates her steps, which include a slip pivot.
Gentleman: "Oh, you have a slip pivot. Let me try something."
They dance the figure again, the gentleman accommodates the lady's slip pivot, and they land on the right alignment for the following figure.
I recently got a new section of foxtrot choreography, and I think I've had this conversation twice this week. Today's tip is to learn your partner's part, regardless of gender or style. In standard, a man needs to know when his partner has heel turns as leading them correctly requires he control his rise and fall in a specific way. Slip pivots always require the partner on the inside of the turn wait/demonstrate a lot of sensitivity to the partner's location. Weaves from promenade require the man to get in front of the lady, and it would help him if she didn't take a monster-size step while he does so.
Feel free to include latin-specific examples in the comments. The principle still applies. Not only while being aware of your partner's part help your dancing; it will also make you a better partner. I have always been hugely impressed when I dance with a partner who knows what my weak spots are and leads to help me overcome them. It is not a common trait in a partner, but a much appreciated one.