Are any problems caused by having the kilogram defined in terms of a physical artefact? (FAQ - Mass & Density)
Yes there are.
The current definition is quite limiting, essentially for three reasons: the International Prototype Kilogram is not perfectly stable (its mass changes with time), the amount it changes cannot be known perfectly (there is no 'perfect' reference against which to judge it) and the values of the national copies cannot be monitored at the highest level of accuracy without being compared directly with it.
As said in a previous FAQ, the kilogram is unique among the seven base SI units in that it is the only one still defined in terms of a physical artefact - and this brings many unique practical problems in realising 'the kilogram' (ie reproducing it) and disseminating (passing on) its mass value throughout the technological World. By contrast, the units of the other six base quantities (length, time, electric current, thermodynamic temperature, amount of substance and luminous intensity) are all now defined in terms of natural constants . (One unofficial, tongue-in-cheek but perhaps useful definition of an ideal base unit is one that can, in theory anyway, be replicated on the other side of the world, to within state-of-the-art measurement uncertainties, simply by e-mailing a description of the physics to another competent physicist. The current definition of the kilogram fails this test.)
While the theoretical measurement uncertainty associated with the value of International Prototype of the Kilogram is zero (it is, by definition, exactly one kilogram) the practical accuracy with which the kilogram can be realised is limited by the stability of the artefact, the repeatability of the balance on which it is used and the repeatability of the nettoyage-lavage cleaning process . Although the stability of this artefact is monitored against a number of copies, the practical limit of the uncertainty in its value is about ±2 micrograms. Additionally, the value of other platinum-iridium 'kilograms' has been seen to drift by up to 2 micrograms per year although the Kilogram is undoubtedly more stable than this.
The fact that a single artefact provides traceability for the entire mass scale world-wide presents difficulties. The large number of measurements needed to calibrate national prototypes (locally held similar-but-not-exact copies of the International Prototye Kilogram) with adequate frequency presents a major logistic and resource problem. The necessary cleaning process - to return the kilograms close to a 'base mass value'  - is not only time consuming and arduous in itself but greatly increases the number of weighings which must be made on each artefact. Mass values of 'a kilogram' before and after cleaning are calculated, as is the weight-gain of such kilograms in the few weeks after the cleaning process. Thus the effort required is very high and the national prototype kilograms are not available to their national measurement institutes (NMIs) for a period of around six months.
Most NMIs around the world hold only one official copy of the kilogram and thus their entire national mass measurement system is dependant on the value of a single artefact. This means that the handling and storage of their weight is very important and any damage means it has to be returned to the Bureau International des Poids et Mesures BIPM for re-calibration or even replacement.
The inelegance of the current system of traceability for mass - to a single artefact - is labour-intensive compared with the fundamental definitions of the other SI units and, with ever-increasing demands of science and industry, is accuracy-limited.