I addition to Francois's post, let me add a few comments. It is true that DEM quality may have a strong impact on the quality of the correlation results, but the influence of the DEM also depends on the incidence angle difference between your images. In short, if you're working with images having small incidence angle difference (<1 degree), you will still be able to obtain good results, although the DEM may be of poor quality. As a rule of thumb, ASTER images with almost exact footprint overlap should have very similar incidence angles.
If optimization of GCP between the shaded DEM and the image fails because of poor DEM quality, you have two possibilities:
1- select a few tie points very carefully and do not optimize them (the good old times method, Francois solution #2)
2- Do not select any tie points and orthorectify your ASTER image without using any GCP. This solution should work fine if you didn't use any GCP when generating your DEM.
As Francois wrote, it is true that you could not use any DEM at all and see what happens (but most likely the results will be impossible to interpret).
Try to use a DEM whenever possible, even if this means not optimizing the GCP, or not selecting any tie-points. Whenever you use a DEM, to make sure that nothing weird happens during processing, the DEM should not contain any "missing values" or unrealistic values. When DEM generation fails, missing values are sometimes replaced with -65535 values, or Nan, etc... Any such values will make your processing to fail, as COSI-Corr will interpret these values as elevations of -65535 meters. You should interpolate the missing values to be within a physical range, although "it might not look good".
For your project, I would then advise:
1- Try to use images with almost identical footprint to minimize potential parallax error due to poor DEM
2- Generate a DEM and make sure it doesn't contain any missing value (interpolate the missing values if needed)
3- If DEM generation didn't use any GCP, do not use GCP either to ortho-rectify your ASTER image, it should give acceptable results. If results are not acceptable (you can check a posteriori if the ortho-image and the shaded DEM overlap properly), you can use tie points, without optimizing them if the shaded DEM visually looks bad.
4- Regardless of the previous steps, you will have to select and optimize GCPs (maybe 5-6) between the second raw image of your project, and the ortho-image generated in step #3.
Hope this help, let us know what worked best for you.