Icons - the icon influence needs a cleaner approach that doesn't overwhelm the GM with loads of encumbering improv (maybe a sliding scale of "level of influence" the icons exhibit). The current system can lead to a table full of positive and negative consequences the GM has to deal with, especially overwhelming if you have a big table and lots of lucky die rolls from players. I think almost everyone I know has had to house rule this to keep it under control. (For those who don't know, each PC has a set of favored, neutral or opposed icons who have a stake in their future; at the start of each session you roll dice and see if there's a chance of a positive or negative interaction that may take place during the night's session. This can get messy, fast.)
It also has another problem: session length. I'll just take my own gaming as an example: I'm in one game that runs on Wednesday evenings, where we in theory play from 7 to 10 pm. But of course, some people are late, and there's a bunch of chatting and catching up before each game, and sometimes we end a little early when we get to something that looks like a fight and it's 9:30 already. So effective game time is something like 2 hours. I have another game that shares some of the same players on Saturdays. We usually get started at like 4 pm, then eat while chatting and stuff, and are ready to go before 5 pm and then keep going until maybe midnight: 7 hours of game.
In a 7-hour game, I could likely find nice places to have 1-3 bits of icon influence. In a 2-hour game? Doesn't sound likely.
Other "per session" mechanics in other games run into the same problem. It's one of the weaknesses of The Troubleshooters: you reset to 4 story points at the start of every session. So short sessions keep pumping in new story points at a high rate, making character weaknesses (which you get story points for triggering) less useful. Worse, most weaknesses can be triggered either for 3 points for inconvenience, or 6 points to take you out of a scene entirely... but a whole scene can sometimes be the whole session, which wastes the points. Another game with a similar mechanic is Star Wars: Force & Destiny, which is about playing Force users. As Force users, PCs are more sensitive to the Light and Dark sides of the Force, and you have a persistent stat called Morality which is about how close you are to either side. You also have a stat that resets per session, called Conflict, which increases when you do questionable stuff (including calling on the Dark Side). At the end of each session, you subtract your Conflict from 1d10, and apply the result to your Morality (so if you don't do anything bad at all you go up by the whole d10, and the more bad things you do the lower your Morality goes). Of course, shorter sessions lead to less Conflict per session, meaning you're likely to go up more.