If your a 'freeze frame' perfectionist, then you might notice the difference between cables, if you search for the odd pixel that might be slightly the wrong shade etc...
With audio you may hear some difference, as there are certainly perceptual differences if you compare a cable with jitter issues and one that is better...
The longer the cable the bigger the risk of bit errors and jitter, especially with a 1080p signal.
But to be honest for the average joe, even a fairly budget HDMI cable will out perform a scart cable by such a high degree that spending more than £20 on short HDMI cable even on a fairly high end TV/Hifi system is pretty pointless.
The physical construction generally improves as you spend a little more, but there really is no point in getting a cable like a £100 monster.. Really a waste of money unless your after a 10 meter+ cable to run to a remote projector etc.
The real time error correction is pretty good, and honestly the cable really has to be pretty rubbish before you get enough errors to be annoying unless as I said your into freeze frame, and sitting 5cm from the screen looking for flickering pixels.
Thats the thing with video... how many people are going to notice a few random errors for 1/60th, 1/50th, or even 1/24th of a second (depending on the hdmi refresh rate). Even if there were 200 errored pixels on every frame, they would likely be in different places... and with over 2 million pixels making up every frame.. and the errors are probably correct enough that the worst you would expect is a perhaps a light red might be a little darker for example...
For short runs really any cable will likely be fine, Im using the free cable from my SkyHD box and it works fine. If buying a 1-5m cable £20 should get a cable that is plenty good enough for 1080p. Longer cables... spend the extra money if you intend to use a 1080p source.
The idea that digital is digital, and it works or it doesnt is wrong, and I take issue when people say digital is perfect... Computers use a lot of error correction systems to ensure data integrity, but audio/video steaming systems consider that the stream timing is more important than an occasional incorrect datablock. Error correction can mask enough errors that most people wont see any differences between the cables.. but if actually measure the signal with an oscilloscope, or actually decoded the signal back into 0's and 1's the cheapest cables would most likely show high error rates... but to most people a few errors doesnt degrade the picture very much.
