Gear Misalignment?

Is this a problem I'm asking anyone who has an opinion - don't hold back.

The main gear and the drive pinion are out of alignment by about 1/4 inch (on the left side). By the corrosion on the main shaft it looks like the pinion did at one time sit about 1/4 inch to the left, which would bring all of the gear-teeth surfaces into full contact. Is that something I should correct? Looks to me like the pinion is shrunk onto the shaft as I don't see any pin or screw holding it.