I frequently see people write "all this", instead of "all of this". Is this a grammatically correct phrase? My intuition tells me that it's wrong (the spoken phrase "all this" is really a contraction of "all of this"); but I'm having a hard time finding any evidence to support the claim.
Yes, it is correct.
This is an example of what linguists call ellipsis, or elliptical construction. Wikipedia defines it as "the omission from a clause of one or more words that would otherwise be required by the remaining elements."
It's fine to omit words in this manner so long as your audience understands what you're saying.
The word "of" implies NOT all, such as half of that, most of these, part of this. All that, all these, etc is grammatically correct !