Let's say an Interest Rate/Discount Curve (SOFR, ESTR, LIBOR or any other) is bootstrapped using the standard inputs and market quotes for Cash, Futures, Bonds/Swaps. What are the metrics to be looked at, steps to be followed and tests to be done in order to validate that the bootstrapped curve is valid and fit for purpose? (any literature or practitioner references would be highly appreciated).
A first step would obvisouly be to check if the curve you built replicates the input instruments.
A second step might be to check the forwards to see if there is irregular behaviour around the curve nodes. Look at a plot of daily 3m or 6m forwards which should be smooth. Different interpolation methods will generate diferent results and for this might I suggest "Methods for Constructing a Yield Curve" by Patrick S. Hagan and Graeme West.
Another good reference on curve construction would be "Everything You Always Wanted to Know About Multiple Interest Rate Curve Bootstrapping but Were Afraid to Ask" by Ametrano and Bianchetti