spoke end poking out of rim, thinking it may be reason why Im getting flats When I run my hand on the inside of the rim, I can feel a protrusion of the spoke end going into the rim. Is that normal?

I have been getting about 5 or 6 flats, and they sometimes occur on the same place, but sometime on totally different place of the tube. I went to my local bike store, and he said to replace the inside rim tape. I had a black rubbery rim tape, and he made me replace it with a white, almost looks like its made out of cloth, rim tape. I put the new rim tape and a new tube but still got a flat.

Then I got frustrated that I needed to patch the tube again and put electrical tape two times over the inside rim, after which I wrapped the new rim tape around again. I finally got another flat in a totally different place and am not sure what to do any more. When I try to match the location on the rim to the hole, I can see that it roughly corresponds to a spoke end sticking out, and there is nothing on the tire when I run my fingers through it. The wheel is pretty old, I got it from a bike restoration shop. The holes in the tube are very small, the only way that I can find them is by filling a container with water and running an inflated tube through it. The tire I have is a Panasonic I got maybe 2 or 3 months ago.

What kind of rim should you have to put the black rubber rim tape and what kind of rim tape should you have when using the white cloth-like rim tape?
If you can see the end of spoke going out of the nipple, you should polish it with a rasp. If you do not see it, but feel with your hand, the tape will be enough (if it put right, as Batman wrote).