  The majority of massive star-forming galaxies at $z\sim2$ have velocity
gradients suggestive of rotation, in addition to large amounts of disordered
motions. In this paper, we demonstrate that it is challenging to distinguish
the regular rotation of a disk galaxy from the orbital motions of merging
galaxies with seeing-limited data. However, the merger fractions at $z\sim2$
are likely too low for this to have a large effect on measurements of disk
fractions. To determine how often mergers pass for disks, we look to galaxy
formation simulations. We analyze $\sim$24000 synthetic images and kinematic
maps of 31 high-resolution simulations of isolated galaxies and mergers at
$z\sim2$. We determine if the synthetic observations pass criteria commonly
used to identify disk galaxies, and whether the results are consistent with
their intrinsic dynamical states. Galaxies that are intrinsically mergers pass
the disk criteria for anywhere from 0 to 100$\%$ of sightlines. The exact
percentage depends strongly on the specific disk criteria adopted, and weakly
on the separation of the merging galaxies. Therefore, one cannot tell with
certainty whether observations of an individual galaxy indicate a merger or a
disk. To estimate the fraction of mergers passing as disks in current
kinematics samples, we combine the probability that a merger will pass as a
disk with theoretical merger fractions from a cosmological simulation. Taking
the latter at face-value, the observed disk fractions are overestimated by
small amounts: at most by $5\%$ at high stellar mass ($10^{10-11}$ M$_{\odot}$)
and $15\%$ at low stellar mass ($10^{9-10}$ M$_{\odot}$).
