[lmr]

Astronomers usually detect them by watching how they make their parent star wiggle, a technique known as the Doppler method.

These planets aren't actually seen, they are 'detected' by the gravitational forces that are present in a system. These planets are hence 'inferred' to be there. Could there be other things causing the 'wobble" like other stars or black holes or something?

[El Gato]

These planets are hence 'inferred' to be there. Could there be other things causing the 'wobble" like other stars or black holes or something?

"Or something" perhaps. Black holes, unless truly tiny, would make their presence known in other ways, although there cases of multiple star systems where one of the "stars" is actually a black hole. Other stars would also be "visible", or at least their spectrum would be.

Basically, if it's considerably lighter than a star, and isn't glowing, then it's a planet, almost by definition.