It's been over a year since I last ran MAID, so my impressions are a bit hazy at this point.
The randomness can bring fresh and unexpected results, which in turn requires some thinking on your feet as a GM. Unless you and your group are very high energy and really into the genre, though, the default mode of play - the "Favour Race" where you just try to curry favour with the Master by performing tasks around the Mansion - can get stale rather quickly. I think my players preferred having meaningful objectives, and weren't of a mind to go into detail roleplaying tasks such as getting the Master out of bed, serving breakfast, drawing the bath, and other minutiae of servant life.
The inter-character competition wasn't a favourite with my groups, either. Our first game had an infiltrator out to assassinate the Master, and our third game had a maid motivated by revenge against the Master. My players are, by and large, happier with games where the whole group gets along and works towards a common cause. This came through a bit with MAID; the first game was just frustrating, although the third game played out quite nicely with revenge served at the very end of the storyline. Maybe it's just a matter of familiarity and forming a suitable attitude.
The general way of thinking for a lot of players seems to be "if my character is disadvantaged, especially if someone in the group causes that disadvantage, it damages my fun because I want to succeed and prosper through my character." With games like MAID (and also FATE, Smallville, and to a lesser extent Tenra Bansho Zero, all of which I'll discuss later), if you approach them in this frame of mind you're unlikely to enjoy yourself. Rather than vicariously experiencing your character's success or failure and becoming annoyed at the lows, the priority shifts. You use setbacks, complications and consequences as opportunities to roleplay intense emotions and define your character - show how they deal with adversity, demonstrate something about them as a person, and really get into the characterisation. Use conflict to ask questions about their personality and beliefs - is this worth fighting for? Is it worth dying for? Is it not as important to them as you first thought?
Of course, this sort of expression is not for all games; a group running a straight-up dungeon raid is likely to roll their eyes if one of the players is constantly expressing angst over the slaughter of innocent humanoids... But if the game is about drama and the free expression of characterisation without regard for group stability, then an appropriate approach is essential. This is why a discussion of the game and expectations of play should precede each new campaign, to make sure everyone is on the same page.
I also think that in games with secrets and rivalry, it is useful for all of the players to know what's going on, even if their characters don't. This was a bit weird to start with, coming from a viewpoint of "I only want to know what my character knows" and trying to cut down on exposure to out-of-character information, but MAID pretty much demands that you be able to hold both in-character and out-of-character knowledge in your brain while keeping them separate. It also encourages players to act on out-of-character knowledge to put their characters in awkward situations, or to make life difficult for someone else, so they can play up their secrets and expose themselves to adversity. That sort of fourth-wall-breaking attitude is difficult to embrace when you're used to playing the game as a simulation of a world rather than an emulation of a narrative structure.
Anyway, a lot of this musing congealed much later on in 2012. MAID opened the door for me to try out new GMing techniques and group dynamics, as well as exercising advice such as "talk about preferences and expectations before the game." It hasn't always worked that well as sometimes players seemed uncomfortable or unfamiliar with articulating their gaming preferences, but over the course of the next few campaigns, I learned more about what sort of games and techniques my players do and don't enjoy.