The problem with Jar Jar is that he is the only character in the film with a full character arc... My fear is that if they "fix" him, the film will focus even more on him - not intentionally, simply because our brains are searching for a specific zero-to-hero stereotype and Jar Jar fits the bill for the most part, just not pleasantly.
I think one of the biggest things missing from TPM was controversy between Anakin and Obi-Wan. Anakin should have known Obi-Wan didn't think he should be trained as a jedi, and been defensive about it and eager to prove himself. They could have bickered slightly, just a few short remarks back and forth. Obi-Wan, over the course of the film, should have grown to grudgingly like him, with the destruction of the Trade Federation ship being a catalyst for him taking Anakin as his apprentice. Including that in the film would have given Anakin and Obi-Wan their own arcs to rival and probably supersede Jar Jar's arc.
Instead we got a "last wish" from Qui-Gon, which left much to be desired...