The problems mainly occur when you have more HDMI devices than your display has HDMI inputs. Then you have to pass the HDMI through a receiver or switcher. In many cases the HDMI handshake/negotiation breaks down and the device won't play at all through the switcher, or it won't support the same resolutions that work fine over a direct connection.

Also, because the audio and video are on the same cable, and each device only has one HDMI output, you're forced to route the video through a receiver so that the receiver can process the audio even if you don't really need the switching. This results in the same compatibility issues as above.

The HDMI standard wasn't forward-thinking enough to handle different audio codecs, so they keep having to revise the standard every time a new sound format comes out. You need HDMI 1.1 for DVD Audio, 1.2 if you want SACD, and 1.3 if you want Dolby TrueHD or DTS-HD. Of course the chips are not firmware upgradeable, so you have to buy new DVD/HD-DVD/Blu-Ray player and a new receiver to get new HDMI chips so you can use the new codecs. Can you imagine if they had to change the ethernet standard and you had to buy a new computer every time there was a new file format you wanted to download?