Using a state‐of‐the‐art 193 nm‐LA‐MC‐ICP‐MS system and with careful control of analytical procedures, the long term external reproducibility and accuracy of the ages Phanerozoic zircons measured over a period of months using calibrator bracketing for the 206Pb/238U and 207Pb/206Pb ages were ca. 1% (2 RSD) if a single reference zircon was used for the matrix‐matched calibration. When different reference zircons were used for the calibration, suspicious systematic shifts in the obtained ages were observed and thus a reduction in the overall accuracy of the dating method became obvious. Such shifts were within a few percent range of the U‐Pb and Pb/Pb ages and seemed to vary independently of zircon age and composition. A “test of accuracy” experiment was conducted reducing instrumental effects as far as possible by analysing five different reference zircons mounted on a single mount eight times during the same session. An identical protocol was used for all analyses, with unchanged instrument parameters and with ion beam intensities kept as identical as possible. For data reduction, every zircon served consecutively as the reference zircon for calibration, with the others in the batch treated as unknowns. The known reference age and the four calculated ages obtained using the four other RMs for calibration were then compared. Even using such a strict analytical protocol, shifts in 206Pb/238U, 207Pb/235U and 207Pb/206Pb ratios were still present. They varied non‐systematically and ranged from −4.35% to 3.08% for the investigated age range (1065 Ma to 226 Ma). Assuming the absence of instrumental effects (i.e., memory, dead‐time correction, non‐linearity of ion counters and interdetector calibration, crystallographic orientation, ablation cell geometry and setup, gas flows), the observed shifts were attributed to matrix and/or ablation related effects. It is proposed that non‐spectral matrix effects in the Ar plasma torch resulted in non‐uniform signal enhancement (or depression?) leading to shifts both in elemental and Pb isotopic ratios. Additionally, the ablated particle size distribution could be an important factor controlling plasma conditions and thus mass bias and fractionation. Until such effects are well understood and controlled, it would seem that any LA‐ICP‐MS zircon U‐Pb and 207Pb/206Pb age determination cannot be meaningfully interpreted at below a ca. 3% to 4% (2 RSD) confidence level.