  Context. It will soon become possible to directly link the most accurate
radio reference frame with the Gaia optical reference frame using many common
extragalactic objects. It is important to know the level of coincidence between
the radio and optical positions of compact active galactic nuclei (AGN). Aims.
Using the best catalogues available at present, we investigate how many AGN
with significantly large optical-radio positional offsets exist as well as the
possible causes of these offsets. Methods. We performed a case study by finding
optical counterparts to the International Celestial Reference Frame (ICRF2)
radio sources in the Sloan Digital Sky Survey (SDSS) Data Release 9 (DR9). The
ICRF2 catalogue was used as a reference because the radio positions determined
by Very Long Baseline Interferometry (VLBI) observations are about two orders
of magnitude more accurate than the optical positions. Results. We find 1297
objects in common for ICRF2 and SDSS DR9. Statistical analysis of the
optical-radio differences verifies that the SDSS DR9 positions are accurate to
~55 mas in both coordinates, with no systematic offset with respect to ICRF2.
We find 51 sources (~4% of the sample) for which the positional offset exceeds
170 mas (~3{\sigma}). Astrophysical explanations must exist for most of these
outliers. There are 3 known strong gravitational lenses among them. Dual AGN or
recoiling supermassive black holes may also be possible. Conclusions. The most
accurate Gaia-VLBI reference frame link will require a careful selection of a
common set of objects by eliminating the outliers. On the other hand, the
significant optical-radio positional non-coincidences may offer a new tool for
finding e.g. gravitational lenses or dual AGN candidates. Detailed follow-up
radio interferometric and optical spectroscopic observations are encouraged to
investigate the outlier sources found in this study.
