Greasy Spot??

http://edis.ifas.ufl.edu/ch015

if pesticide didn't alleviate the problem, try a fungicide.

What's the deal with that split in the fruit?

@rhizo_1:

I should've been more explicit, but that is part of my question (indicated by the word "blemishes" in the title of the thread). Indoor or outdoor, my citrus fruit has been rapidly ripening and then getting these blemishes before becoming fully ripe, even after several applications of pest killer. It has been concurrent with the sticky substance on the fruit. It has so far happened to a half dozen fruit on two trees. I've never seen anything like this before. I'm about to go to the store to get some copper-containing fungicide to apply to the trees. Soon I won't have any fruit left!

Did you check the pictures in my link?

Keep scrolling down and youll see the picture of the fruit. It looks similar to your second pic.

@blazeaglory - yes, i did take a look, and do see the resemblance. the plants have been sprayed with the antifungal spray

Have you been having any cold spells lately?

About 95% of the split citrus I"ve seen is from uneven watering. Too dry too long followed by too much. The problem is made even worse with some tight skinned fruit. Container grown outdoors also contributes in warm climates. Lemons are not usually victims since most have thick spongy inner rinds.

What area are you in?