In order for a cable to uniformly change a video stream that looks "better" or "worse", the random bit changes of every 10bit value would have to somehow decode to uniform changes in the resulting 8bit value. Chances of this happening - ZERO.
While it is indeed erroneous (or at least extremely imprecise) to characterize data errors in a digital transmission system (HDMI/DVI) in the same terms that we associate with an analog system (i.e. component or RGB video) . . . it's also important to understand that TMDS is no different than other digital modulation/encoding schemes in that in order for it to work properly and deliver uncorrupted data, certain electrical conditions must be adhered to in the cable and connection.
Electrically, HDMI uses multiple shielded twisted-pair cables within a single jacket, and supports a bandwidth of 350 MHz (HDMI 1.3). Main cable vulnerabilities include high differential skew between pairs, high crosstalk, incorrect impedance, and poor bandwidth . . . in addition to classic cable issues such as high ground resistance (causing hum components to be imposed on the data).
So in terms of cable quality, there may be any number of issues that may or may not surface for any given application. For instance, does it meet the same specs in all lengths for which it's available? Is the production consistent between different samples? Do the connectors mate securly and reliably with those of many other manufacturers? Does it maintain its performance in electrically noisy environments? When twisted and flexed? When it makes a small-radius bend behind a flat-panel TV?
As always, humans have an infinite capacity to cut corners and make things cheaper, and HDMI cables are no exception. For that 1-meter length that's easily accessed for replacement, a cheap one may suffice . . . but for a 40-foot run up through the walls and attic to a projector? Well, if you don't mind crawling up there to replace it if you start having problems, then maybe a cheap one there is fine as well . . .