How should I handle measurement errors in a timeseries database?
I would keep the data, if at any point in the future you want to find out what was wrong with it you still have it.

It can provide you with some information later on about how often measurements fail, where they originate from, what the offset is and things like that.

Deleting the data is unrecoverable, handling them in some way can always be changed later on. For example you could handle them in your client application for now and if you have some issue with that store them physically in a table_cleaned table.

If you deleted them or replaced them with NULL the information is gone for good.