A way to improve the intro of JarJar occured to me:
Qui Gonn is seen running from the droid transports when suddenly, there's a Gungan in the way. "Get out of the way!" he yells ineffectually and they comically "trip" over each other.
That does two things wrong: first off, it lets Jar Jar into the movie (a mistake we cannot correct) AND it makes Qui Gonn look dumb. Why doesn't he Force push that goofball out of the way or do something cool like that?
What we can do is cut out the shot of Liam Neeson gesturing ineffectually and whining "out of the way! I'm a Jedi running for my miserable life and you're in my way!"
More heroic would be to have Qui Gonn simply running -- seeing Jar Jar in the way, too terrified to run -- and tackling Jar Jar as a way of saving Jar Jar's life. He tackles Jar Jar on purpose, (as Jedi should do everything). He sees the way to save the poor CGI creature and does what he must. No flailing and whining.
This straightens out this odd beat and strengthens the sense of debt that Jar Jar feels for Qui Gonn.