In subsequent years, they're supposed to apply a formula, but of course "drift" can occur. And then there's an appeal process.
Doesn't this just incentivize people to not pull permits on major work? In California contractors often try to talk you out of getting a permit because it's more of a hassle for them, so clearly the contractors aren't liable for doing unpermitted work...
For DIY'ers, there's actually a nice program... once you pull a permit, you get to talk with the code inspectors during their office hours, and they will walk you through everything you need to do in order to meet code. A friend of mine built an entire addition this way.
There's no way to hack-proof any taxation mechanism.
If it's not to code, it can take many visits to get a full list of issues.
There is little thought given to how much the individual house is worth, rather it relies on comp sales in the area. For example, a fully renovated house might go for $500k, but another in the neighborhood with the same number of bedrooms and bathrooms in a less desirable location (say the entrance to the neighborhood) might only be able to sell for $400k.
It is also very common for the adjustments upward to be far quicker than adjustments downward.
Then there are definitely examples out there of the city appraised value being driven by desired tax revenue and becoming detached from the reality of sale prices.
If you remodel, you are suspose to have your property reassessed.
My current house was being taxed at a value of 1/8 of what I paid for it.