Well I think the mechanic has messed up.
Had a bad rattle under the truck when going up hills or under a load.
Took it to a local mechanic and he found the issue within 10 minutes.
The center driveshaft bearing was worn out.
Had a bearing picked up and the same guy installed.
I watched and it didn't seem like a hard job but.
After he put the bearing in the noise went away and now I have a terrible vibration when accelerating.
Looked in my book at the procedure he performed.
Now I know I'm in trouble because he didn't mark either place, front or back.
I'll see if there happens to be a paint mark or maybe a ascribed mark but if none can be found I don't know what to do.

 

Welcome to the site...

Be sure the yoke is/was re-installed on the coupling shaft in the same orientation as it was originally installed. The orientation is critical so that proper driveshaft balance and U-joint 'phasing' is maintained. It's a good practice to install on the OE paint index when available, but we replaced many shafts, yokes with new and the factory index was long gone, and wouldn't cause a severe condition.

 

Remembering how the mechanic did the removal.
He took the bolts out of the old center bearing.
Took the bolts out of the back driveshaft where it attaches to the rear end.
Then he took loose the axle yoke that attaches to the back side of the front drive shaft, on the back side of the center bearing.
Then he pushed the back shaft forward slightly and dropped the back shaft out.
Then he removed the 4 bolts that hold the front shaft to the transmission.
And removed both the front driveshaft and the center bearing.
I remember noticing the new bearing didn't turn as freely as I thought it should.
The first time he pressed the bearing on the shaft, you couldn't turn it by hand.
He then took it off again and noticed he had put the wrong dust washer on the wrong side of the bearing but could never get it off again.
Don't know if that means anything or not.
Now all this being said, I'll try and take the yoke cap off that he took off and maybe rotate the shaft 180` and re-attach.

Is that what you were talking about?

 

Here is a picture of the center bearing looking from the back of the truck. He took this yoke loose before taking the old bearing off.
Is taking both sides loose and rotating the shaft 180` an idea to try?

 

Seems something wasn't done right, or was overlooked.
Looking at your image, it looks like the u joint seal is crumbling/blown? They look very old or OE, were they checked?
So,, you can jack up and support the truck rear,, and have someone bring the RPM/Speed up to about where you would feel the vibe. Apply the rear brake slightly to simulate driveline 'load'. It usually will simulate road condition, load, and help diagnosis a possible cause. You can try re clocking the flanges etc, but generally a shaft out of balance is more of a harmonic issue, not a severe conditions unless something is wrong. You can rebalance a shaft, but if you visibly see it running un true then something else needs attention..

 

Also in your images, I can see where the old flange centering tab marks on the u joint bearing cups were rotated (clean area on the bearing cup) . On a new joint, no big deal, but on a bearing cup with heavy rust and debris, and the retaining clamp then pulling the cup against the flange tab can pinch the u joint tight/zero clearance. Just something to check, but the joint in the image almost looks like the u joint leg is no longer centered in the cup. Meaning, its done if so..

 

Well I took the back drive shaft out and rotated it 180'. Checked the U joints very carefully and they seem in great shape. No wobble and very smooth. I lined up the caps on each end to be assembled where they were originally. The shiny part that was in the original flange. Checked the center bearing and it was very free and smooth turning while the transmission was in neutral.
Drove about 6 miles and the noise has been reduced a huge amount. Still I can hear a little roar when increasing speed just before changing gears (right around 2000 rpm).
Checked the fluid in the transmission and all was good. Now I'm wondering what it will take to completely fix the roaring sound, I think I'll drive for a few days and recheck the bolts and inspect it all again.
Not wanting to open a can of worms but the chances of taking the spline out and rotating is still an option. But it only happens while accelerating. 2nd to 3rd and 3rd to 4th. No issues when I get to highway speed.

I called the local Ford dealership and they told me just about everything for my truck has been marked obsolete and they can't help.
Thanks for all the comments and suggestion. You all are great.
Lesson learned. Mark all shafts before disassemble.

 

Does this mean to remove the spline end of the shaft and rotate 180 degrees?

 

Before you get concerned with a balance problem, you MUST repair the problem with the U-Joint which has been pointed out.
Once the seals show ANY signs of problems, which these stand out like a sore thumb, the only fix is to either replace them yourself or have them replaced.
There is a right way and wrong way to replace U-Joints and beating the caps in with a hammer is definitely the wrong way. The needles can fall out and one missing needle is just as bad as a badly worn U-Joint.

You may find that might be the source of the vibration problem.
Playing around trying to balance a shaft that has bad joints is an exercise in futility and a waste of time and $$$.
If you do it right, you will do it once.

 

I appreciate the candid and informative answer. I'll need to research how to change that U-Joint since it looks like a complex job.
Thanks again,