This is the first of two papers describing the observations and cataloguing of deep 3-GHz observations of the Lockman Hole North using the Karl G. Jansky Very Large Array. The aim of this paper is to investigate, through the use of simulated images, the uncertainties and accuracy of source-finding routines, as well as to quantify systematic effects due to resolution, such as source confusion and source size. While these effects are not new, this work is intended as a particular case study that can be scaled and translated to other surveys. We use the simulations to derive uncertainties in the fitted parameters, as well as bias corrections for the actual catalogue (presented in Paper II). We compare two different source-finding routines, OBIT and AEGEAN, and two different effective resolutions, 8 and 2.75 arcsec. We find that the two routines perform comparably well, with OBIT being slightly better at deblending sources, but slightly worse at fitting resolved sources. We show that 30-70 per cent of sources are missed or fit inaccurately once the source size becomes larger than the beam, possibly explaining source count errors in high-resolution surveys. We also investigate the effect of blending, finding that any sources with separations smaller than the beam size are fit as single sources. We show that the use of machine-learning techniques can correctly identify blended sources up to 90 per cent of the time, and prior-driven fitting can lead to a 70 per cent improvement in the number of de-blended sources.