Astrometry is one of the main pillars of astronomy, and one of its oldest
branches. Over the years, an increasing number of astrometric works by means of
Hubble Space Telescope (HST) data have revolutionized our understanding of
various phenomena. With the launch of JWST, it becomes almost instinctive to
want to replicate or improve these results with data taken with the newest,
state-of-the-art, space-based telescope. In this regard, the initial focus of
the community has been on the Near-Infrared (NIR) detectors on board of JWST
because of their high spatial resolution. This paper begins the effort to
capture and apply what has been learned from HST to the Mid-InfraRed Instrument
(MIRI) of JWST by developing the tools to obtain high-precision astrometry and
photometry with its imager. We describe in detail how to create accurate
effective point-spread-function (ePSF) models and geometric-distortion
corrections, analyze their temporal stability, and test their quality to the
extent of what is currently possible with the available data in the JWST MAST
archive. We show that careful data reduction provides deep insight on the
performance and intricacies of the MIRI imager, and of JWST in general. In an
effort to help the community to devise new observing programs, we make our ePSF
models and geometric-distortion corrections publicly available.Comment: 22 pages, 18 figures, 1 table. Accepted for publication in PASP. The
ePSF models, geometric-distortion solutions and codes are available at the
links provided in the manuscrip