You will start to get lost lines, or parts of lines, when the error rate gets worse that what causes sparkles. If it gets worse, the screen may blank.
Let me change my original comment after thinking about it a bit. The best thing would be a certified high speed HDMI cable. There are no passive cables that will do the trick. It would have to be an certified high speed active HDMI cable. These are HDMI cables with built in equalization designed for the specific cable. These are beginning to show up on the market. They should handle any HDMI signal you can throw at them, including 4k at 8 bit color depth.
One would think think that there would be a plethora of devices that use fiber or Cat cable that would be as good, but most of them seem to be limited to 225 MHz clock rate, which is well below the HDMI maximum of 340 MHz. The lower clock rate can be problematic when running 3D, deep color, or in the future 4k. There is also the problem that Cat 5/6 cable is just not as good for the purpose as HDMI cable. It would take properly grounded Cat 7 cable to match HDMI cable performance.