HDMI cables will make an obvious difference like yours, where there is dropout, and flashes, but HDMI cables will not produce better colours, brightness, or contrast like some people have posted, and like some companies suggest. Even What Hi Fi have made the mistake of making such claims.I would have agreed with most yesterday that expensive cables are a rip off... but...
I have a bit of a complex routing which see's for example, a Sky box go to an amp then to a distribution unit which feeds 3 screens, 2 off 15m cables and 1 of a 7.5m cable.
Now I've only just put the amp and the last TV in circuit and with some cheap cables the picture was horendous! The 15m cables are better quality and give no issues but the new cheap short one really didn't work! Not so much your regular analogue style interfearance, but massive bright spots on the screen, the picture even kept on dropping out! On shorter more direct high quality cables, I had no such problem.
Anyway, the company are replacing with high quality alternatives which should arrive today, so I'll be able to do side by side screenshots even. Hopefully the new ones will work and give me a solid picture!
So alas, I would agree that on short runs, with simple connections and minimal other devices to interfere, you shouldn't have any problems with cheap cables. Digital indeed should be less prone to interferance... But on longer ones, where there are lots of connections, I can guarantee the cable quality makes a difference!