Does electricity cause damage on a cellular level?
Regarding the moss or lichen on the third rail on British train lines: there is no current passing through the moss/lichen as they are not completing a circuit. They are just sitting on one connector. If another connector passed over them, completing the circuit across them, then a current might pass across them for a very short time. But I doubt they grow on the top of the rail (which is the contact part in the UK system) as that is constantly being polished smooth by the contacts from trains sliding across it.

Regarding cell damage: Apart from fibrillation in animals, and burns caused by Joule heating, electricity does cause cellular damage. 

At low frequencies (&lt;10kHz), electricity disrupts cell membranes and makes them much more permeable (we actually harness this when we use electroporation to transform bacteria). All organisms rely on electrochemical potential differences across membranes for their metabolism (Berry, 2002). The exact effect is dependent on the previous electrical state of the cells, for example the electrical potential difference across the membrane, and on the surface area to volume ratio of the cell (greater volume relative to surface area leads to more disruption). In any case, extreme electroporation can cause solutes to flow in or out of a cell, and generally disrupt the balance of solute concentrations and cause organelles and other bodies to move out of a cell. When the electrical stimulation stops, the contents are then fixed in a disrupted state. The cell then has to expend enormous amounts of ATP using ion channels and transport proteins in an attempt to reinstate the necessary chemiosmotic potentials, and in doing so exhausts the entire ATP supply and goes into biochemical arrest (no metabolism occurs), which is when a cell is dead. Dead cells break apart because there are is no maintenance occuring.

At higher frequencies (10-100kHz) proteins become permanently denatured. Many proteins carry charges which give them an overall polarity. When placed in an electric field, the proteins reorient themselves and will undergo conformational change to achieve the optimum dipole moment in the direction of the field. Ion channels and pumps are particularly sensitive to these disruptions (since their charges are crucial to their function).

Rather than provide lots of references, there is one excellent review from which I drew all this information, and which you should read for more of the physical detail (Lee et al., 2000).

References:


Berry, S. (2002) The Chemical Basis of Membrane Bioenergetics. Journal of Molecular Evolution. [Online] 54 (5), 595–613. Available from: doi:10.1007/s00239-001-0056-3 [Accessed: 9 February 2012].
Lee, R.C., Zhang, D. &amp; Hannig, J. (2000) Biophysical injury mechanisms in electrical shock trauma. Annual Review of Biomedical Engineering. [Online] 2 (1), 477–509. Available from: doi:10.1146/annurev.bioeng.2.1.477 [Accessed: 9 February 2012].