Though, in general, what you all are saying is true, the quality of cables do matter to some extent. For example, if your cable length is over 30 feet, cheap cables may not even carry HDMI signals at all. Even for short distances, I would prefer to use a cable I have some confidence in.
HDMI actually sends the picture pixel by pixel, uncompressed, so dropouts can happen on individual pixels. If these dropouts are bad, a whole line could disappear, or you could see a frame jumping.
With particular regard to AV, HDMI uses what is called TDMS (Transition Minimized Differential Signalling) to carry AV data. This is across 12 pins of a HDMI connector. Pins 01 to 09 carry the AV data, while pins 10 through 12 carry a clock signal. Now this very critical as the clock synchronizes between the audio and video. If the clock signal is dropped you will get lip-sync issues. For example, at home yesterday, I have playing a HD version of Rush Hour. Whenever a chapter changed, I would get the sound first, and the video a few seconds later. This did not happen in every movie. I changed the cable (that came with the player) with a branded cable, and the issue disappeared.
Unlike computer networking, communication between AV equipment through HDMI is not always two way. At the beginning, the receiving station sends what is called Extended Display Identification Channel (EDID). This information tells the sending station what kind of data the receiving station can accept. Once this is set, then the data flow is one way. Unlike computer networks, where the communication is dynamic and continuous, the receiving station in an AV system cannot ask for resending of AV data if the checksum is incorrect. Data loss, if any, is thus absolute.
Though the data moving between the two stations is digital, also remember that cable sees it as just an electrical current. If the cable has bad conductance, it can lose data. The longer the cable, the more the danger of losing data. Similarly if the connectors are not made well, seating could be an issue, and any of the nineteen odd pins in HDMI may not have a proper contact. If the conductivity of the pins are suspect, again you have will have issues of data travelling in whole. You could lose pixels of video information, or hear stuttering of audio, as well as see lip-sync issues.
I am not arguing for expensive cables. Just cautioning members that even for HDMI, quality can be an issue. I have seen extensive differences between cables in co-axial digital, optical digital, component, as well as HDMI.
When I spend 50,000 on a receiver, 50,000 on a TV, 20,000 on a player, I certainly will not insert a cable that I suspect.
Cheers