Hello Wall-e and thanks for your post.
As my pal, Steve Ornellas pointed out below, there really is no such thing as an "as is" contract in California since all home sales are subject to the rights of inspection. The only time such rights are removed is when the buyer purposefully removes that contingency with the offer--a strategy that is sometimes employed to "strengthen" the offer in a multiple offer scenario.
Provided your inspection and condition contingency was not removed with the offer and remains intact, you can certainly cancel the contract within the contingency removal period, the default of which is 17 days after the execution of the contract.
However, as Steve noted below, perhaps the better strategy would be to negotiate the repairs with the Sellers. Assuming you really like the home and want to purchase it, working with the seller to get the property fixed is perhaps the best method to resolving these problems. The shower pan, the bathtub and the pool heater are relatively minor repairs and it might be to the best interest of all parties that these repairs be negotiated. Only if you cannot negotiate a resolution on the matter would I recommend canceling the purchase.
Talk with your agent about your concerns, and get his/her opinion on how to proceed! Good luck.
Grace Morioka, SRES
Area Pro Realty
San Jose, CA