  The sensitivity available to near-infrared surveys has recently allowed us to
probe the galaxy population at $z\approx 7$ and beyond. The existing {\em
Hubble} Wide Field Camera 3 (WFC3) and the Visible and Infrared Survey
Telescope for Astronomy (VISTA) Infrared Camera (VIRCam) instruments allow deep
surveys to be undertaken well beyond one micron - a capability that will be
further extended with the launch and commissioning of the {\em James Webb Space
Telescope (JWST)}. As new regions of parameter space in both colour and depth
are probed new challenges for distant galaxy surveys are identified. In this
paper we present an analysis of the colours of L and T dwarf stars in widely
used photometric systems. We also consider the implications of the
newly-identified Y dwarf population - stars that are still cooler and less
massive than T dwarfs for both the photometric selection and spectroscopic
follow-up of faint and distant galaxies. We highlight the dangers of working in
the low-signal-to-noise regime, and the potential contamination of existing and
future samples. We find that {\em Hubble}/WFC3 and VISTA/VIRCam $Y$-drop
selections targeting galaxies at $z\sim7.5$ are vulnerable to contamination
from T and Y class stars. Future observations using {\em JWST}, targeting the
$z\sim7$ galaxy population, are also likely to prove difficult without deep
medium-band observations. We demonstrate that single emission line detections
in typical low signal-to-noise spectroscopic observations may also be suspect,
due to the unusual spectral characteristics of the cool dwarf star population.
