We can't really speculate without seeing some pictures of the problems.

<I applied home made compost to several plants in my yard and some of the turned yellow here and there.>

What kind of plants are you referring to?

Describe the compost - what went into it? How old?

I am confused why do you first say <Anything wrong with my compost?>

Then say <I'm using my homemade compost for many years.>

Instead of asking "What happened to my plants?" Is it the same compost that is many years old? I don't see the yellowing you mentioned.

Do you know something we don't?

That Basil looks as if a sap sucking pest has had a go at it, possibly aphids. I don't think it's anything to do with the compost. Look under the leaves and see what you can find.

I agree that it looks like pest damage....aphids, spider mites, and eriophyid mites are all possibilities.

Pests would make new growth curly? And @Gumby... As I said, it is a cold pile and I am not able to use it more than once a year. I was thinking that it may have not been cured enough or something. I assume that when I use a new batch every year, that it may be different from the year before plus I changed the location of the pile.

I doubt that cold compost up to a year old is going to cause the problems you're describing. The only time compost causes trouble that I've seen is when it's put on when still steaming hot.