Agreeing with Hymoki. Live mixing isn't about "fine" adjustments, but about getting everything to be audible and understandable. It also depends on what live mixing you have in mind. Mixing sound for a venue means making sure the band sounds good, effectively defeating hall's acoustics. Mixing for TV or radio means making everyone's speech clear and opening and triggering playout machines according to schedules.
You are limited by equipment of your console and even those most expansive ones don't have anything fancy. EQ, filters, dynamics section (usually compressor, gate/expander and limiter), panning, all per channel. Sometimes you can get SW plugins ro HW equipment (preffered for reliability) for stuff like delays or reverbs ... but in boradcast those are used just really rarely. Can't speak for venue mixing too much.
You usually also have to rig your stuff, mic everyone, make sure no wireless equipment is classhing in the air and that everyone has full batteries. Also in broadcast it's quite common that audio guys take care of communication equipment for production people. That means configuring intercom matrixes, setting up communication panels and beltpacks wherever it's required and so on...
