I didn't used to have any trouble with the "invisible threads, but now using the monoply polyester from Colonial, which I really like the look of, I found it was looping itself around the peg underneath the spool and making terrible messes if I used the spool horizontally. I found that if I used a finger to lift the thread gently as I sewed it was fine. So, a paperclip fixed it all! Found I could do it two ways - on top of the spool or under the spool!
I kept my tension reduced a bit and took the felt pad off the spool peg. Here are some pictures.
Sometimes if you just play around a little....
