Hesitation and jerking when shifting gears

CK. the ft. rear end by draining some gear oil out an look at it spread out on white paper or sent it off for ani. some turn in drive shaft is ok but not much?

 

Truck and engine make and year?

 

A ujoint that loose would make a heck of a vibration going down the road. I agree with baha, check out that front drive axle. They used to have magnetic drain plugs, dont know if they got cheap and didnt use them on newer trucks?
With that much slop, you should find a bunch of scrap metal hanging off that plug! Analyze it with your eyes, lol.

 

There will always be some rotational play in the driveline. I would check both diffs as they both receive 50/50 split of the power. Internal damage to either one could cause excessive play. It wouldn't hurt to check for excessive rotational play in the slip yokes/u-joints and check for metal in the transmission as well. There are a lot of moving/wearable parts between the flywheel and the hubs. If the truck has high miles on original components it could even been a little bit of wear in everything contributing to a large amount of slop over the whole drivetrain.

 

You might have bad fifth wheel side pins.