I have some Continental gator skins, and I got a tear on the tire where I got a flat, the inside seems fine, but do I patch the inside anyway? I'd hate to replace them, they are expensive!

Only if the hole is large enough for the tube to come back through the tire, then it should be replaced.

Not in the inside, just the outside. The inside just has a very small hole, the size of a needle.

You can drive a tire down to the threads before its worn out. The rubber just provides grip. So if the threads are still solid - just drive it.

Flex the cut open and look into it to see if any of the cord is cut. If so you might want to reinforce the area from the inside. If the cord is fine, glue the cut closed or, if a chunk of rubber is torn out use some filler. The tread rubber provides traction and protects the cord which gives the tire it's strength.

It sounds like you're just seeing the rubber of the outer tread skin flexing open. Provided there's no cut threads at the base of the cut the only downside to that tear or cut is that it may tend to pick up stones easier and it'll let water wick into the thread casing more easily.

I believe if you do a search you'll find some threads in this mechanics forum about gluing such tears together using CA "superglue" or similar.

It's not uncommon for my tires to have multiple small tears or cuts where shards of this or that have cut the tire. And I certainly don't bother repairng puncture holes in my tires. But I admit that if I had a cut that was much longer than about 3/16 to 1/4 inch long in the rubber tread layer I'd try some options for glueing it back shut. But only if it doesn't have a lot of cut through fibers at the base of the cut.

I use rubber cement.

Between 1/8 and 3/16" I just put a couple of layers of duct tape over the hole. For large cuts on a tire with a fair amount of tread left I super glue a piece of 1/32 ' gasket material meant for pipe flanges over the hole. I cover that with duct tape because the rough edges caused by the glue will fret through the tube. I have used this method on cuts up to 1/2". I only use a tire repaired with the glued on patch on the rear. I have never had one fail.
The gasket material is good for 200 or 300PSI in it's design service..

Thanks guys! I used rubber cement. I didn't notice it and haven't had an issue. Thanks for clearing up the anatomy of a bike tire!