I have a bunch of observations of the same object at different times (e.g. for an asteroid). According to the SkyCoord documentation
Inputs may be scalars or lists/tuples/arrays, yielding scalar or array coordinates (can be checked via SkyCoord.isscalar).

So I assumed that I could have a coordinate array with the ra,dec and obstime inputs being lists:

path=SkyCoord([5,10],[20,30],unit=u.deg,obstime=['2017-01-01T00:00','2017-01-01T00:10'])

This initially seems to work:

In[14]: for i in range(len(path)):
...         print(path.ra[i],path.dec[i],path.obstime[i])
... 
5d00m00s 20d00m00s 2017-01-01T00:00
10d00m00s 30d00m00s 2017-01-01T00:10

but it actually doesn't

In[15]: print(path[0].obstime)
['2017-01-01T00:00', '2017-01-01T00:10']

And things can go bad in other ways. The conclusion is that you can't have multiple obstimes in an array coordinate.

So to clarify the documentation, I suggest adding the word:
**Coordinate** inputs may be scalars or lists/tuples/arrays, yielding scalar or array coordinates (can be checked via SkyCoord.isscalar).