I've created a visual tracker of their influence / favour with individual factions. By default they start at -1 with each of the factions, as they gain favour with one side, they will almost invariably start running into trouble with the other factions and have to decide who to make an enemy. If they want to get in really close with one faction, they will end up making serious enemies of both other factions.
Faction reactions just use 2d6 like morale rolls, modified by favour and PCs personality (wisdom or charisma or ...)
Faction Table v1.0: 2d6+Pers+Favour
<2 - terrible, faction will take special steps to remove PCs2 - very negative
3 - negative
4 - negative
5 - neutral
6 - neutral
7 - neutral
8 - neutral
9 - neutral
10 - positive
11 - positive
12 - very positive
12+ - exceptional, faction will take special steps to help PCs
Watch this space for more thoughts.
And a version for grayscale printing and taking notes: