I was thinking that even though TPM is supposed to be the first movie in a series, it never really introduces us to anything. It just assumes we all know what Jedi are or what the Force is. Even Yoda, a character who turns out to be a big player throughout the saga, is never introduced as the important character he is.

Maybe it's an idea to have Qui-Gon explain the Force at some point in the movie, and not the Midichlorian talk he has with Anakin before they leave for Naboo.

It might work if Qui-Gon explains the Force to Jar Jar, while they're riding the sub. It might make the ride in the sub a bit more useful, and expand on Jar Jar as a character. He could be more of a curious character than a clumsy one, and his curiousness is what keeps getting him in trouble and banished.

Dialogue for this scene could be taken from Qui-Gon's original scene with Anakin, and there might be some useful Jar Jar dialogue in the Clone Wars animated series.