We're not talking about lawsuits here, we are talking about finding a mutually acceptable resolution to a minor crisis. This is a cosmetic problem that cannot be resonably repaired. The cost of the vanity top (assuming it is a single sink vanity) is going to run somewhere between $100-$200 depending, plus a bit more to install it if you can't do it yourself, which isn't too hard.
Offering to pay the landlord $100 for the mistake will probably make the landlord happy as a clam. If not, negotiate.
If you land in court on an issue like this its because your landlord is in fact Landlord Guy, and isn't willing to be reasonable.