Given that gravity bends the path of light, how confident can we be that galaxies are where they seem to be? The widely known phenomenon termed gravitational lensing is believed to curve space, thereby affecting the path followed by light and other electromagnetic waves.

This effect is associated principally with galaxies and galaxy clusters, as it requires considerable mass. But in theory any star or star cluster, or black hole, can have this effect to some degree.

What can we tell for sure about the position of external galaxies, if we are uncertain that their light is actually coming to us along a straight path: i.e. if light follows the curvature of space, and that curvature is not uniform, how can we be sure we are not observing, for example, the light from a single source appearing to us as more than one object.

Can a galaxy appear to be in more than one place in the sky?
The widely known phenomenon termed gravitational lensing is believed
  to curve space, thereby affecting the path followed by light and other
  electromagnetic waves.


and gravitational waves! In fact, the paths followed by light and other massless particles (for the lack of a better word) are called null geodesics and they have in common that $$\mathrm ds^2 = 0, $$ i.e. the 4-distance they experience is zero.


  This effect is associated principally with galaxies and galaxy
  clusters, as it requires considerable mass. But in theory any star or
  star cluster, or black hole, can have this effect to some degree.


One could argue that the Shapiro delay is of the same nature, only temporal rather than spatial. You can observe the Shapiro delay from the sun using radar probes!


  What can we tell for sure about the position of external galaxies, if
  we are uncertain that their light is actually coming to us along a
  straight path: 


It is by definition! The path that light takes is straight, even if it seems bent to us in 3-dimensional space. Therefore, galaxies appear where they are because that's where they are. It's just that we project our idea of Euclidean (i.e. unbent) space onto the sky!

I know what you want to ask though: How can we be sure that the sky isn't curved in some insane way somewhere and we're actually looking somewhere else? We do assume that on the whole, space is Euclidean. 

Well, on the small scale this might be the case: We might be looking at stuff whilst it is "really" somewhere else (note that it is really there, the "really somewhere else part" is just us imposing our coordinates on the sky!!).

But we know beyond reasonable doubt that the Universe, as a whole, is more or less Euclidean. At least up to redshift z~1000, i.e. about 300,000 years after the Big Bang. We can observe the Cosmic Microwave Background, and it tells us something about the curvature in the sky. We know that there's structures there which have a certain angular size, as we know that they had 300,000 years to form and we know the speed at which they formed. So we can predict their typical size, and it turns out that the angle under which they appear would be bigger if the universe were oblate/hyperbolic and smaller if the universe were closed. They are just right for a flat universe. So we know that on big scales, space is indeed Euclidean. It might not be the case for individual stars, galaxies, etc. but on average, it works. And cosmology / gravitational lensing usually works with averages and statistics.


  Can a galaxy appear to be in more than one place in the sky?


Totally. There's a plethora of cases of multi image lens-source systems. You can usually sort them out by looking at their spectra and checking their time-variability.