Bought new headlight bulbs, ONE is still dim on my sons 2007 Mustang GT

Does your vehicle have daytime running lights (not sure if any states require them)? I have had some real funky things happen to my headlights in another ford vehicle I own when the control module failed. If you do have day time lights, you can just unplug the module to see if the problem goes away.

You probably do have an electrical issue, but though I would just mention the daytime running light thing just in case all other troubleshooting come up dry.

You have not said, but I think that drivers side would be dim, either high beam or low beam if it's a ground issue. Is it true that both high and low beams on that side are dim ?

I am not great at electrical yet do have the wiring diagrams book in my hands.

As for aiming....somewhat near the connector, rear of headlamp there's another black piece of plastic...with smaller white plastic within. This white plastic has a hex inside of it, and inside of that hex is a place to put a phillips screwdriver. The screwdriver goes into this white plastic...holding the screwdriver in a vertical position.
This adjustment is for vertical of headlamps...what you've stated you want to adjust.

These headlamps do have a sharp cutoff of light at the top of their beam, making it difficult to see ahead if they are not adjusted so that beam is high enough. Others would not agree...but for me, on my car, I've adjusted the low beams so high, in order to see down the road, that I don't use the high beams at all, as they are up in the trees. I adjusted beams several times. trying different heights, until oncoming traffic seemed to be bothered least, yet I can see great with just low beams on.

I'll pm you with my phone number...May be able to help on the phone better, diagnosing weak headlamp issue.

Note: I've now sent a private message twice...yet it does not show me it's been sent...have no clue..what's with that ?

I have seen some threads on here about the stock headlight wiring being fairly light gage ; and if you replace it with heavier gage wiring it really helps with the headlight output. There are kits available for this . . . I don't recall the name of the kit, but some searches here and/or Google should find it.

I know this is not exactly your problem, because it would be the same on both sides, but I bet that if you replaced the harness it might solve the issue because you would be going through all the connections at the same time.