There are lots of things that a home inspector can't be aware of when they inspect a home.
1. For instance, if the temperature was below 65 deg the day the inspection was performed, the AC unit cannot be run at this low of temp and therefore any leaks would not of been found.
2. If it wasn't raining the day of the inspection, or the day before, leaks in the basement would not of been found. Especially if they were from behind any walls that were built or any storage that was in place.
3. Threee way switch problems are really easy to fix and not worth your money suing over.
4. If the rot in the sink base was obvious, then this should of been caught, but if it was covered up with stuff under the sink at the time of the inspection, then it wouldn't of been found. An inspector is not obligated to move anything in the house to perform the inspection.
5. How is the furnace leaking? CO gas? Need more details on this one. Plus, what is the age of the furnace. Look at the inspection report and see what comments were made concering the furnace. If it's greater than 15 years old then a comment should of been made that it's reached the end of it's useful life.
6. The inspector should of placed a drain cover over the shower drain and ran the water to test for leaks. If it was a really slow leak then it would take some time for it to appear in the cieling, maybe more time than what the inpsection took, in this case it's hard to hold him liable.
The disclosure forms filled out by the seller should of listed all the problems with the home. Look over the list, if there are things on there that have failed, and the seller said it was all ok, then they are liable. But, you have to prove that they knew about it and committed fraud when filling out the paperwork.
Look over the inspection report really well to see what area's were highlighted as problems.
One last thing, what state are you in? Home inspectors aren't licensed in every state and the rules are different.