Yes, there are bad effects of heavy load of energy saving lamps. The Compact Fluorescent Lamp (CFL) for instance distorts the current (the main reason for that is inclusion of electronic components in its electric or electronic ballast). It increases the value of the Total Harmonic Distortion (THD) of the current and thus increases the THD of the voltage. This effect appears when they are intensively used. For that reason some CFL producers add (within the lamps) circuits of power factor correction and harmonics reduction, which somewhat reduce their bad effects.
However, they have advantages when compared to Tungsten lamp (TNG) as the CF lamps consume only 20% of the power consumed by TNG lamps giving the same illumination level. As well as they have longer life (although number of switching affects it). The harmonics which they generate increases the losses by an amount of 29% under the condition of same illumination level. So, regarding the power, even with the power loss due to the harmonics, still they consume less than TNG lamps. Regarding the current and voltage distortion which they cause, more effort is required to reduce or eliminate the effect on the power system.
For the case of the same wattage replacement, no saving is achieved, as system losses will be higher, besides voltage regulation will be worse, installation cost of distribution system as transformer, conductors, protection devices will be higher, and voltage distortion will be higher.
I am still investigating comparison between the long Fluorescent lamps (the one with magnetic ballast), and the Compact Fluorescent lamps, and I think the gap (in terms of power loss) will be narrower.
A conference paper entitled:Study of Load Side Harmonics Sources Effects and Elimination, which may be useful, is within ResearchGate in my page. You will find the CFL lamp named Electric Ballast Lamp.
I am assuming that by "energy saving lamps" you mean lamps using electronic ballasts instead of magnetic ones, such as Fluorescent lamps, CFL and LED lamps. In such cases, the lamp ballasts draw distorted input currents, but the harmonic content depends on the product and can vary widely. The existence of large harmonic current causes the current waveform peaks to be large and also present a poor power factor to the power system. Large current peak demands can distort supply voltage and also cause tripping of overload relays. The poor power factor causes higher current demand with higher heating loss in the supply system. When switched on, they also have large 'inrush' currents due to initial charging of their internal dc bus capacitor. The combined inrush current of a heavy load can cause unwanted tripping of breakers.
In addition to the previous answers, I would like to contribute with regard to the frrequency bands. It has been clearly described that non-sinusoidal signals will be present as the CFL and LEC lamps operate, either in voltage as current. At least two frequency bands can be clearly observed: low frequency harmonics (below 2 or 3kHz) and higher order frequency components (>2kHz and