Before I get into anything, please note that this thread is for the discussion of possible house rules based on reviews and session reports (no, I have not played the game yet - will be doing so for Christmas) for feedback from the community after preliminary plays. Yes, I will play with the Rules As Written for at the very least my first game (with one exception) so I can get a feel for things, but I wanted to share these ideas with people to see what the consensus might be "hypothetically speaking".
So, to start, the one and only rule change I will be implementing in my first game:
Scene of Crime marker
Visiting the Scene of Crime marker allows you to "get a jump on the case" by handing the First Player token to any player. This costs 0 time.
Based on session reports and reviews, it seems that it's actually more beneficial to go last in turn order for the sake of your plots. I also reduced the cost of getting a jump on the case to 0 time to make it a more attractive option.
Then possibly for future games:
Evidence tokens
Before the game begins, remove all negative-value evidence tokens from the game.
A common complaint in the reviews I've read so far is that it is too difficult to mentally keep track of which suspect might be the most guilty at any given time. It seems that a large contributer to this would be the fact that evidence tokens can make a suspect's guilt go down as well as up. With no negative-value tokens, a suspect's guilt will always go up, just by slightly differing amounts. This also makes the Reporter's and Snitch's abilities more useful.
Alibis, surprise witnesses, purjury and strong/weak files
To accommodate the above rule change:
At the end of the game, when calculating the guilt of each suspect, one evidence token of the highest value is removed from the suspect's "weak" file, and one token of the highest value in the suspect's "strong" file is doubled.
A surprise witness token in a file "cancels" one token of the highest value in that file. A purjury token coupled with a surprise witness token will double that token instead.
An alibi token cancels the evidence token of the highest value anywhere on the suspect.
Turns, Time and the First Player token
Instead of passing the time sheet around, place it in a central location where it can be reached by everyone. At the start of each day, each player places one of the character tokens on the "0" time space. As investigators use time, they move their marker up the time track (rather than down) to keep track of how much they have used. Once a player reaches their maximum time for the day, they may not take any more actions or turns.
Instead of a player taking all of their actions uninterrupted as their turn, a player's actions will be split up across multiple turns over the course of a single day. A player's turn now consists of:
1) One or more movement actions, then
2) One action of any other type.
Therefore, a player may make multiple movement actions as the first part of their turn to move across the board quickly, but then take only one "other" action.
The order players take their turn in is determined by the time sheet. Whichever player has so far used the least amount of time this day will be the next player to take their turn. In the case of ties (as will be the case at the start of each day), the player holding the First Player marker decides the order players take their turns in.
This makes the First Player token much more useful, meaning that detectives will be visiting the scene of the crime much more often (as, thematically, they should do). It also reduces downtime, gives players more opportunities to interrupt each other's plans and makes the whole time mechanic much more interesting.
Light/Dark cards
When you play a light card on yourself, you dark-shift your character, as usual. However, when another player plays a dark card on you, instead of that player light-shifting their own character, they light-shift your character.
The mechanics for light/dark-shifting at the moment seem to be designed to encourage as much card play as possible - there doesn't seem to be any reason not to play any cards you may hold in your hand. This rule change makes the playing of cards more of a tactical choice - you can play a light card on yourself, but then you open yourself up to other players playing dark cards on you. According to session reports, dark cards are very circumstantial anyway, so this would still be a gamble you would be willing to take.
Anyway, those are my initial ideas for Android house rules. Please tear them apart as you see fit based on my grand total of zero plays so far (just please don't reply with "play the game first", as I'm well aware of that already).