For what it's worth:
So far I've read two predominantly negative critiques. Anticipation and Flattening and Frodo on Film.
The odd thing is that I find myself agreeing with almost every point made and yet I can't help but feel that by focusing on the parts the transcendent whole has been missed.
Sassy, the "Anticipation and Flattening Essay" (full name "Mithril Coats and Tin Ears: 'Anticipation' and 'Flattening' in Peter Jackson's
The Lord of the Rings Trilogy), which was written by the book's editor, Janet Brennan Croft, was one of the two essays in the book that I disliked intensely. Croft has a decent grasp of Tolkien, and a valid point of view about the films, but I felt that her purpose to cut down and criticize the films was so obvious that it eliminated any ability to take her arguments seriously. This is exacerbated by a number of highly misleading and downright incorrect statements that she makes about the films.
This sense was made worse by the fact that this essay follows one that is guilty of the same faults only even worse. "Summa Jacksonica: A Reply to Defenses of Peter Jackson's
The Lord of the Rings Films, after St. Thomas Aquinas" by David Bratman, reads like a bad parody of an extended post by a m00bies purist. It is so biased in its approach that no reasonable editor would have included it a compilation meant to be scholarly. It is only because Croft's own opinion matches Bratman's that it was included.
At this point in reading the book, I was about ready to give up, particularly since glancing through the rest of the essays revealed that most of them had a negative take on the films. Fortunately, I perservered, and while I found much to disagree with in some of the rest of the essays, there were no others that I found to be written from an overly and unacceptably biased point of view.
That includes the "Frodo on Film" essay that you mentioned (full title "Frodo on Film: Peter Jackson's Problematic Portrayal"). This essay, written by Daniel Timmons, has the advantage of being written about a specific subject. Timmons approach is pretty straightfoward, and fairly accurate from my point of view. His basic conclusion is one that I agree with:
In the end, both Frodos "were meant" to bear the burden and to "find a way" when no one else could. Thus, both the book and the film dramatize the themes of divine designation, pity, mercy, forgiveness, and self-sacrifice in the portrayal of Frodo. The difference -- and it's a significant one -- is that Jackson wants to appeal to a contemporary audience, and so, for the most part, offers a "hero" with whom he thinks "the masses" can relate. On the other hand, Tolkien presents a special character, albeit not a perfect one, whom we can admire and aspire to become. Frodo's doubts, fears, sufferings, and flaws may parallel our own. Yet through steadfast courage, dogged plodding, humility, and faith, we may discover the strength and wisdom to bear our own burdens and to envision our ultimate state of grace: "a far green country under a swift sunrise".
I don't necessarily agree with Timmons on all points regarding the lessening Frodo's character in the films, but I do agree with his basic premise. Unlike Croft (and even more, Bratman) his descriptions of the events and characterizations of the films are mostly fair and balanced. In the end, I felt that made his overall criticism of the films all the more powerful and convincing then theirs.