While it is true that inspectors are all required to carry E&O Insurance, it is not likely to be used in this case (plumbing repair about $200-300, drywall repair about $150-250: Typical Insurance deductible limit $2500). The real question you need to determine is what the condition of the area was on the day of the inspection. Maybe there is a photo or description of it in the report?
Is it reasonable to assume that the area was obscured from view? Is it possible that the leak is newer (mold can grow quickly) and was not present or was very minor at the inspection? Is it possible that the shower was not used frequently enough by the previous owners to produce the leaking effects that you noticed? Or, is it simply bad luck that it recently broke under your new ownership?
If there was an attempt to conceal the damage (new paneling or drywall or recent paint) then that would indicate the owners knew and did not disclose it. If there was no indicaton they atttempted to cover it up, then it is quite possible they did not know of it and could not have disclosed it (you can't report what you don't know about).
Similarly, if no one saw the damaged area at the inspection or final walk through, or if the area was obscured from view at the inspection, then it is very possible that the condition wasn't able to be seen by the inspector.
If you determine that the inspector reasonably should have identified this problem, then you should review your inspection contract. Most inspection contracts have a clause that tells you what to do in event of a claim - typically they say to call the inspector and offer him the chance to view the condition as soon as possible after you discover it (DO NOT GET A REPAIR DONE BEFORE THE INSPECTOR REVIEW). The inspector can then respond to your complaint and you can work out the matter between the two of you.
Of course, as others suggested, you always can contact a real estate attorney for a legal opinion on the matter. My help is simply anecdotal and from a practical standpoint as an inspector.
In case it helps you, I have received calls from clients with similar concerns after they move in. Most times, I am able to help them understand why their concern wasn't able to be identified during an inspection. Often, it doesn't make them happy (it's not the "I'll pay for it" answer they were looking for) but at least they understand what happened and why, and why it wasn't noticed on the inspection(sometimes it is, and they just ignore it - but that's another case entirely!!! ;-) )