Why don't Mei and Leo act like they recognize each other in the Peony Pavilion? There isn't anyone around to keep up the charade for.
Perhaps they were afraid that someone were eavesdropping upon them.
When you're the most expensive girl in a high-class whorehouse, you can bet that there's always going to be some security within earshot. Their failure to turn up during the swordfight notwithstanding.
The troper figured that Leo and Mei were both staging a fight so that the Flying Daggers members hidden in the Peony Pavilion (as its' implied the showgirls are Flying Daggers members and don't seem to reveal themselves at the beginning to help Mei) could flee to their hideout. If so, it's not explained quite well. The Pavilion lady does commend Mei for setting a trap for the government officials in the end.
The much bigger question is why Mei tries to kill Leo. Keeping up the charade that he's not with the Flying Daggers? Who would even suspect it? And breaking her own cover? Who gains from that? And it's not like she doesn't know she's going to lose the moment she grabs his sword. Is it some pathological S&M fetish that overrides both honor and reason? From a trained assassin so committed to her craft and her cause she gives up her personal life to be a blind sex worker?
It got her into custody, which gave Jin a reason to rescue her. Leo, as far as most know, is a talented guard who helped save the Emperor. Wanting to kill him out of revenge is not out of the question.
It seemed to be part of the plan as it did not bode well for the Flying Daggers when government officials swarmed the Pavilion. As it appears the showgirls were Flying Daggers Members, Mei's and Leo's swordfight allowed them to escape and run to the hidden base in the forest as they were at the end.
Said Flying Daggers (the weapons) apparently can do anything when tossed. Including attempt three times to hit a target, going around a shield while in midair and requires at least four shields to be blocked. So, what keeps their leader from tossing one of said daggers to the Emperor (or whoever they wanted to assassinate) and kill him in one shot!?
With the insane physics-defying they do, simply dropping one straight down should have done it.
Why does Mei still pretends to be blind while facing some poor mooks which she's going to turn into mincemeat anyway?!
In case someone shows up who she can't kill without breaking cover.