My father has a 94 Jeep GC and blew a tire in another state. He had a tire put on that wasn't the exact same size as the other. After a few months the front diff. started acting like a locked differential. Low speed turning on pavement is ugly. Any ideas about what I should look for when I open it up?

I don't think you will have any problem seeing what went wrong when you open it up.

Would burned up spider gears be the only thing that would cause the axle to act like a locker? I was guessing that someone else had seen what happens from a wrong size tire and if they were able to fix it without replacing the diff.

You most likely will get away with rebuilding the one you have. Dr diff could give you a better answer.

What transfer case? My bets the viscous coupler is bad.

This

I don't know which transfer case it has other than stock.
I get it, like leaving my manual trans truck in 4WD on pavement.
How would I test it's coupling?

Take the time to identify what case you have first. On the case there is a round tag that will have the model number stamped on it.

The transfer case is a NP 249 J. I also picked up the 1994 factory service manual today!

Here's a pic of the tag. It's a 249 case. I just noticed some yellow paint in the corner of the pic. Might be a junk yard swap from the previous owner.
How can I test the viscous coupling? It looks like a $500 part so swapping the whole thing will be cheaper if that's the problem.

We need Scott Smith to ID that cocoon thing.

There is no real test that I am aware of that conclusively pinpoints it to the viscous coupler. For the most part it is the symptoms. The hotter it gets the worse it gets. Binding on turns especially if you drive in figure 8's at a parking lot. The tires will bind and chirp. Depending on miles a used one may not be much better. For sure these type transfer cases need 4 tires identical in make and size.

kinda looks like a mud wasp nest.

You can pull the front shaft, if that fixes the problem then you can count on it being the t-case.

I don't think its good for them but they can be driven without the front shaft. I know when I used to follow the jeep stuff closer the 5.9L grand Cherokee guys would do this so they could do burnouts lol.

Thanks everyone. I was thinking it was the diff. and hadn't considered the transfer case. A trip to the junkyard is in order.

I guess you could always pull the rear driveshaft and see if it still does it. If it still does it, it would be the front end. Easier yet, just jack up the front and try rotating one wheel. The other side should rotate in the opposite direction pretty easy.