Written registers are a reasonably recent thing in human language, so the peculiarities of written language would qualify as innovations.
The catch is, the characteristics of written language I can think of are matters of degree, rather than categorical differences from spoken language. But they include things like syntactic complexity, anaphora referring back a long way, intolerance of ambiguity (because of the lack of access to immediate feedback), and notions of periodically structured sentences.
, MA in Linguistics from BYU, 8 years working in research for language pedagogy. and
, Linguistics PhD candidate at Edinburgh. Has lived in USA, Sweden, Italy, UK.