  The standard cosmological parallax--distance formula, as found in the
literature, including text-books and reference books on cosmology, requires a
correction. This correction stems from the fact that in the standard text-book
derivation it has been ignored that any chosen baseline in a gravitationally
bound system does not partake in the cosmological expansion. Though the
correction is available in the literature for some time, the text-books still
continue to use the older, incorrect formula, and its full implications are not
yet fully realized. Apart from providing an alternate correct, closed-form
expression that is more suitable and convenient for computations for certain
limiting cases of FRW ($\Lambda=0$) world models, we also demonstrate how one
can compute parallax distance for the currently favored flat-space
accelerating-universe ($\Lambda>0, k=0$) cosmologies. Further, we show that the
correction in parallax distance at large redshifts could amount to a factor of
three or even more. Moreover, even in an infinite universe the parallax
distance does not increase indefinitely with redshift and that even the
farthest possible observable point may have a finite parallax angle, a factor
that needs to be carefully taken into account when using distant objects as the
background field against which the parallax of a foreground object is to be
measured. Some other complications that could arise in parallax measurements of
a distant source, like that due to the deflection of incoming light by the
gravitation field of the Sun and other planetary bodies in the solar system,
are pointed out.
