EDIT: On a related note, when I was an undergrad there was a group on campus that was doing research on how humans repair garden-path sentences when their first reading is incorrect. They were measuring ERPs to see if something akin to a backtracking algorithm was used + eye-tracking to see which word/words triggered the repair. I graduated before the work was complete, but I might go digging for it to see if it was ever published.
EDIT 2: Apparently this is better researched than I realized: https://en.wikipedia.org/wiki/P600_(neuroscience)
The solutions to these low-level problems seem to be unimportant for high level tasks. Not to mention that error propagates. Error on part-of-speech tagging will propagate to dependency parsing that uses that info, and eventually this error will affect NER or entity/relationship extraction and similar.
[0] https://en.wikipedia.org/wiki/Garden-path_sentence