Just to start...
Changed stellar patterns (new constellations, etc), different planets visible, possibly differences in the star they are orbiting, unless it is the same size/distance/class. Earth would figure out really dang quickly that it had been relocated.
We have our skies and our solar system pretty well mapped out. If that changed, we'd notice in a big hurry. Even if the new system was unrealistically similar to the Sol system, we'd notice that planets weren't where they were supposed to be, and weren't the same planets, probably within a day.
And travelling through a wormhole is bound to give us some really weird signals, so there's that as well.
In short, modern humanity would notice. Heck, the ancient Chinese and Mayan civilizations would notice...even the Druids who built Stonehenge would notice.
EDIT: Thought of another few things...
Unless we were dropped into the same 'spot' in our orbit around this new star, it would make our current season go all wonky (swap from winter to fall rather abruptly). It'd take time for the temperature to reflect the change, but it would definitely be noticeable and might take a little while to re-stabilize. And unless the race that dropped us into our new orbit was exceedingly precise about it, our weather would see some changes if our seasons ended up altered. If we had a more or less eccentric orbit, or if our axial tilt relative to the new star was different.