I always play minecraft with Mekanism in 1.7.10.
Every time entering to play the world, Mekanism says the update news of 9.1.1 version for ONLY "1.9 or 1.10".

I'm pretty certain there is a config option to check for mod updates. Turn that off and it will stop annoying you.

Their is an update to 1.7.10 but it is a failed build that did not get pushed out.

We should not need disable this as what happens when a new 1.7.10 version is released? We would never know! :(

Can we by default have the update checker NOT check for different minecraft versions, and make sure it is also not checking for failed builds?

Once Aidan uploads Mekanism to Curse, I'll keep up with updates by seeing and clicking on a green 'download update' button. :P

My 'turn off the config' was intended as a temporary workaround. I agree that it would probably be a good idea for Mekanism to not try searching for updates in other versions of Minecraft.

This is done in 1.10.2 versions, checks are done based on game version instead of universally as they were done before. Disabling "UpdateNotifications" will solve your issue for now.