With the exception of some of the solid core ropes, the 'knots' are all eye-splices that put the bulk of the load down the rope when tied correctly. A knot, however, puts a lot of force into squeezing your rope, and can definitely create a weak point if ridden on. That being said, for general wake-boarding, the chances of you busting a rope even with a knot in it are pretty slim, as you're not typically putting a huge load on the rope.
The only place I see ropes break somewhat frequently is in the show skiing world, but it's almost exclusively at the dock start (and often-times can be due to a knot), when you could have a 600+ hp triple-rig pulling 25+ people off a dock. I've broken my spectra barefoot rope as well, but it was doing a barefoot flying dock start when I didn't see a knot catch. As soon as I hit the water it snapped right at the knot. A couple new eye splices though, and only lost a foot off that rope, and it's still in use.
For that t-handle I wouldn't worry about that knot weakening it too much, as it's got a pretty decent size radius to the turns. Also, if you want to fix your frayed rope, cut out the bad section and tie in a couple loops. This is a good video on how to
https://www.youtube.com/watch?v=y3da6pgU2R4