""Do web servers get bad sectors? "" - I don't know, but I would think it advisable to assume that they might. A program of preventive maintenance - eg. replacing drives well before their MTTF - might help lower the chances. I think it is possible to monitor the recording quality, so that blocks where retrieval confidence is falling can be taken out of use before they fail and drives with high levels of bad blocks can be replaced.
I would also expect that the web hosting service provider would mitigate their effects, should they occur.
The recording on the disc could incorporate redundancy to effect error detection and correction.
Redundant arrays of discs could cope with uncorrectable errors.
If, despite all precautions, live files were corrupted, I hope there would be a backup so that service could be resumed quickly. (Though this is really just another type of redundancy.)
A lot depends on Service Level Agreements. The more important data availability is, the more people will pay and the more you can spend on precautions. Probably nothing will keep the site up when the sun becomes a red giant, but until then I think it's just a question of $$.