I beg to differ. The Jedi were but the cream of the crop in my opinion... In the Old Republic Jedi Order, there were a lot of younglings trained in the Jedi Temple who never were selected for Padawan training; they were not taken as padawans because of multitude of reasons but mostly I bet it was because while they were force-sensitive, there were people better suited to being Jedi Knights, so they were sent to menial task forces to do whatever, from agriculture to some security forces I would think.
Like with any other skill or attribute, force-sensitivity is obviously not an on/off feature. After some point, the being becomes aware of the force, and I concur to the point that Han Solo hardly exceeded this limit, especially without training and meditation. He might have become aware of the force, to some extent, with training from young age... his sensitivity might or might not have been enough to become a Jedi, we don't know.
So, it's a question of definitions - if you want to define "force-sensitivity" as an ability to be aware of the force, then so be it. My definition to force-sensitivity is a bit more loose - to me it just a position somewhere on the line between a shrimp and Anakin/Luke Skywalker. Granted, there might have been Jedi Shrimps, but I find it a little far-fetched, even despite Yoda's continuous bitter talk about size being unimportant.
Obviously personality also affects how much of the force potential the person is able to use - ability to concentrate and dedicate themselves to training, and so forth. If one believed the Force to be hokey-pokey religion, they would hardly try to use it consciously. Unconscious guidance from the Force is another thing. And I find it plausible to think that Han Solo might have had better force-sensitivity than your average Corellian smuggler, but not enough for him to spontaneously start sensing the Force and consciously use it. Or maybe not, but in that case the character shield problem remains a glaring huge plot hole. If Han Solo was even somewhat more sensitive to force, his good luck in firefights would have at least some degree of credibility.
But I've made my opinion clear enough already. Perhaps someone should ask about it from Lucas or something. Although I have a feeling that the answer would be something along the lines that anyone can form their own opinion about what's going on there...