[TTBlows]

I have a thump type noise in my bronco when I drive slowly over rough terrain. I was looking underneath and found that if I push up on the area where the two ujoints go into the rear of the transfer case the whole section moves up and down. It appears that there is a bushing or something worn in the rear of the transfer case.

Sounds like your tranny mount may be worn. Take a closer look as you push up on the t-case. If you can't find one locally, I got mine from rockauto.com

Also take a close look at the 12pt bolts which connect your d/s flange to the t-case flange. These will back out if not lock-tited and can cause a definite clunking (btdt).

It also sounds like your double cardan may be in need of a rebuild, the centering ball or pin may be worn. The ball can be replaced. If it's the centering pin, you're better off to just get a whole new d/s.

 

[TTBlows]

The tranny mount is shown here, between the crossmember and tailshaft housing:

There's some pics of the double cardan rebuild here:
http://www.superford.org/registry/vehicles/detail.php?id=139&s=13394#content

 

[TTBlows]

There shouldn't be any slop where the flange comes out of the transfer case should there?

I've sometimes noted 1/16" to 1/8" of fore/aft movement, but there should be no vertical movement, no.

 

[TTBlows]

Can I do this in my garage without pulling the transfer case? It looks like it shouldn't be very hard.

Yes and yes. Just support the tranny or t-case with a jack, unbolt the xmember and swing it down (easy on E4OD models), replace (use loctite!) and reinstall