Are there any bright non-stellar objects which make up asterisms? Hopefully the title is very self-explanatory. I was wondering if there were any non-stellar objects, such as bright galaxies, which when looking with the naked eye were mistaken for stars in the time when asterisms were documented and catalogued...

For example, within the Big Dipper I believe it is Mizar which is in fact a binary star system. (Correct me if I am wrong!)  

I was hoping perhaps for distant yet bright Messier objects being mistaken for stars...
Most of Messier's objects are too dim to be seen by the naked eye. The few that are visible were mostly listed as stars in older lists. 

Edmund Halley lists 6 "luminous patches" which "discover themselves only by the telescope, and appear to the naked eye like small fixt stars" (Halley).

These include M42, in Orion, part of the sword (or what ever that is between the hunter's legs), and Omega Centuari, listed as a minor star in the centaur (roughly on the horse's back) in Bayer's list. 

(The other objects on Halley's list were either known to be "cloud-like" [M31] or too faint for naked eye astronomy.]