It’s not unreasonable that an untrained Force sensitive kid might learn to do a few parlor tricks like pulling a broom to his hand without ever being able to do much more than that. Interestingly enough, it’s those kind of parlor tricks Anakin does around Padme in AOTC, even though he says Obi Wan frowns on such frivolous use of the Force.*
*We later see Obi Wan use the Force to open and close doors mere inches away from his grasp. Which makes him out to be a bit of a hypocrite. 😛
I mean, those could just be the automatic doors you see everywhere, and he’s just like the rest of us. 😛
On Kamino, he clearly does the Force hand wave at them. The shot in ROTS when he’s concealing himself in a compartment on Padme’s ship is the biggest offender.