If you take your move action before you use your standard action to fire a ranged weapon, do you suffer from some kind of penalty? And what if you do this via the Shot on the Run feat?
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No, there are no penalties. There's no place in the rules I can really quote here, because it simply isn't considered. The assumption is that if you both move and attack, your movement does not interfere with the attack. There are no combat modifiers related to movement, and it isn't mentioned under either the movement rules or the general combat rules
The same goes for Shot on the Run. (The feat represents the special training your character has to accomplish the maneuver, after all!)
There are explicit penalties when shooting from horseback:
Keep in mind that, generally, if you take a ranged attack and a move, you've spent roughly 3 seconds aiming. That seems like plenty of time for a trained adventurer!