In a flurry of new moon discoveries in late 2000 and early 2001, it was
announced by this author – and several other sources – that the planet Uranus
had 21 moons. Now it comes out that that is not "officially" the case.

One object, S/1986 U 10, has been passed over for the official "moon"
designation by the International Astronomical Union (IAU), the internationally
recognized authority for assigning designations to celestial bodies and any
surface features on them. The criteria for obtaining official moon status has
changed over the years and is now much more strict. The object in question was
discovered in 1999 by Dr. Erich Karkoschka, after he studied 300 Voyager 2
images of the Uranian system taken in 1986. If the object, given the
classification S/1986 U 10, had been discovered shortly after the Voyager 2
flyby, it’s moon status may have been confirmed. Instead, the object wasn’t
discovered until 1999, after tighter requirements were put into place. The IAU
now would like a Hubble Space Telescope image of the potential moon, before
confirming its existence. That image could come in the next couple of years.
Until then, the official moon count is – as of 12/18/2001:

Number of Moons in the Solar System (12/18/2001)

      Mercury - 0 moons      Mars    - 2 moons    Uranus - 20 moons
      Venus   - 0 moons      Jupiter - 28 moons   Neptune - 8 moons moons
      Earth   - 1 moon       Saturn  - 30 moons   Pluto - 1 moon

S/1986 U 10 stats:

S/1986 U 10 was discovered by Dr. Erich Karkoschka with the Lunar and Planetary
Institute in Tucson, Arizona. Karkoschka had detected the faint object in 7
different Voyager 2 images. After carefully calculations, he determined that
S/1986 U 10 lies between the two moons Belinda and Puck and has a very eccentric
orbit.