It's the GM's responsibility, I think, to read every word that is written, to interpret the sum of the characters' actions, and to ensure everyone involved understands what's happening and why. Even great players who read everything commonly misinterpret other players' posts, so everyone reading everything isn't necessarily the solution to all problems.

I've had a couple players tell me that it felt like [i]cheating[/i] to read posts that have nothing directly to do with their character, which is an understandable mindset. In a large group, reading everything can feel extremely confusing, since the narratives are never in exact chronological order.

When I GM I run under the assumption that players will only read what is directed at their character. I've experimented with quoting key points from players' posts, summarizing everyone's locations/actions in the mod post, and encouraging @Mentions in everyone's IC posts, with mostly positive results. The OOC is a great tool for discussing what's going on, too.