Euclid is an ESA mission to map the geometry of the dark Universe with a planned launch date in 2020. Euclid is optimised for two primary cosmological probes, weak gravitational lensing and galaxy clustering. They are implemented through two science instruments on-board Euclid, a visible imager (VIS) and a near-infrared spectro-photometer (NISP), which are being developed and built by the Euclid Consortium instrument development teams. The NISP instrument contains a large focal plane assembly of 16 Teledyne HgCdTe H2RG detectors with 2.3μm cut-off wavelength and SIDECAR readout electronics. The performance of the detector systems is critical to the science return of the mission and extended on-ground tests are being performed for characterisation and calibration purposes. Special attention is given also to effects even on the scale of individual pixels, which are difficult to model and calibrate, and to identify any possible impact on science performance. This paper discusses a variety of undesired pixel behaviour including the known effect of random telegraph signal (RTS) noise based on initial on-ground test results from demonstrator model detector systems. Some stability aspects of the RTS pixel populations are addressed as well.