Do you know what the various resolutions are of your TVs? If so, can you please post which ones work / don't work?
I called Apple today & they said it was a resolution incompatibility issue.
I'd used my 32" LG TV for years as an external display on my old 2008 MacBook Pro until around the time I upgraded from Mavericks to Yosemite.
I upgraded my MBP models twice in less than a year to resolve the problem. Last week, I bought a model A1398 retina because it has 3 ports that support displays (2 Thunderbolts & 1 HDMI) After I couldn't get ANY of them to connect, I called Apple (today).
After troubleshooting for an hour or 2, the Apple tech asked if I had another display & I tested the A1398 model on the 60" Samsung in the living room. The HDMI connection worked. The Thunderbolts didn't. I didn't have an other few hours to sort that out, so I'm happy to know that something works.
After I hung up, I wondered why a resolution issue would affect the HDMI port, but not the Thunderbolt ports.
Now I'm wondering if I really do need a new TV, or if there's something else (obviously, a lot of people in this forum got a lot of other things to work).
You were the only one I saw with LG TVs & other brands to test, so maybe you'd have some idea whether resolution could be the problem or not.
On your TVs that did work, did each one open a 2nd window in Display Preferences? (that added a "appearance " option to Display/Color options bar)? If so, did either window recognize your display by brand name?
Since there isn't a drop down menu with compatible brands/models, I'm curious to know if Yosemite automatically recognizes all compatible external displays by brand name (or model, or resolution, or some other clue about what's compatible?)
I can't find any display resolution controls on my TVs, & Display Preferences in Yosemite doesn't show that option either, so none of that helps me determine ... anything.
I'd think that if resolution really is a compatibility issue, that there would be an easier way to figure out which non-Apple external displays will work. But then, maybe that's their intention - to get us to buy only Apple products.