Why is the security for the brothel completely horrendous, especially considering that violence towards sex workers is a real life issue, you would have thought it would have been thought out in more detail? There's a single bodyguard, Argent, a woman who could easily be overpowered by any strong male (moreso if there's a group) but here's a short run down of her failings:
She fails to search every client who walks in. This is a common practice in every real life brothel - people can easily hide a weapon and attack the prostitute. The whole point of being a prostitute at a brothel and having a pimp is for the protection you wouldn't otherwise get if you were a streetwalker or working alone. Clients just walk in and out as they please.
She allows Gilder, a man clearly armed to the teeth, to come in and go off with one of the prostitutes. Good thing he wasn't insane or anything... Actually she wasn't even in the room when he came in (this goes back to the fact that anybody is allowed to walk in) and nobody thought "Hmm... this man is carrying multiple knives... I should get somebody in case he's dangerous..."
She allows Rhys, clearly angry, to storm about the brothel, shouting at people, kicking down doors, throwing out another client (who doesn't complain because she's physically frightened of the man) and punch a prostitute in the face (which causes a fight).
I seem to recall Argent trying to intervene when Rhys stormed into the Teahouse, but Claret restrained her from going into Axis's room. And she further didn't intervene in that case when it was clear that Rhys and Axis were having sex.
Following on from the second point: she has no idea what's going on in any of the rooms because she's the only bodyguard. What if Gilder had stabbed Linneus: she wouldn't have been able to help him because she didn't know about Gilder, the fact he carried weapons and if he had hurt Linneus she wouldn't have learnt about it? Instead of being at the door, trying to protect people within the brothel, she stands either in Xanthe's room or outside it because...
She allows Rhys to fight and rape Axis all the while Axis shouts for him to stop, gets overpowered, tied up and raped. Twice.
Axis wasn't raped. Word of God has already spoken on this subject and have implicitly stated that rape doesn't occur in the comic.
Remy, in chapter five, sneaks into Rory's room without his knowledge. Do the doors not have locks? Who's protecting the place while Argent is asleep?
WMG time. Remy and Rory haven't had the rosiest of lives; it wouldn't be far-fetched to suppose Remy knows how to pick locks. Alternatively, she procured the key from her superiors, or has access to it by the virtue of being a maid with room maintenance duties.
She leaves the brothel unattained while she goes shopping at the beginning of chapter five. Meaning there's nobody there to look after the place - not that she did a good job to begin with.
What people need to keep in mind is that the Teahouse is a relatively small brothel. There's only six courtesans working there, and when Argent went out on the shopping trip she was guarding half of them. Atros was at the Teahouse during the trip, and he can be pretty good at defending himself. As to why she didn't intervene with Remy and Rory—why would she think she needed to? They're twins, after all, and Remy puts on this air that's she an innocent waif. If Remy goes into Rory's room, I'm pretty sure Argent isn't going to think anything of it.
Why does Gilder stay at the brothel overnight? Prostitutes are paid by the minute and usually an hour is the maximum. Let's say Linneus costs $200 an hour. Did he really pay $1600 just to sleep? Because they're shown sleeping later (and in the bonus bits in the book).
Probably because he's not staying anyplace else at the moment? It's not unheard of to spend the night in a brothel.
It's been implied that his life consists of getting money and blowing it on booze and whores. Secondly, renting a hotel room and paying to get a whore there for the night might actually be more expensive, seeing how the brothel isn't providing any service besides the whore and his room. Third, Gilder was pretty smitten with Linneus, he might have well left earlier if that weren't the case. Fourth, there's no need to assume that Gilder spent a 1600-dollar night sleeping after one quick 'do...
Why the hell is Claret one of the lowest earners? She's cute and well-endowed, has a bright and bubbly personality, has excellent customer service skills and is very happy to please. Hell, when the line-up bell is rang she's the only one who seems to actually want to be there. And yet for some reason she's portrayed as incompetent and barely earning her right to stay at the house, when in actuality she should be rolling in clients. Meanwhile, Lilith is the highest female earner, despite being snotty and disinterested even to potential clients.
Because there's a ton of shiptease between Claret and Argent, some fans theorize that customers sometimes don't order Claret because they get a Death Glare from Argent.
Because Teahouse specialises in male whores and there probably are other houses with wider ranks where fans of busty, genki girls get what they like. Lilith probably shows a world of a different face to her preferred and/or regular customers. Her snobby attitude would support that idea.