There are several things that you might want to check for.
Fortunately for you, there's a spreadsheet that I (Becky) have written which does these things.
For example, rootlet intrusion, soil type (e.g., limestone carbonates), and handling of the specimens in the field or lab (e.g., accidental introduction of tobacco ash, hair, or fibers) can all potentially affect the age of a sample.
Bioturbation by crabs, rodents, and other animals can also cause samples to move between strata leading to age reversals.
Gove consulted numerous laboratories which were able at the time (1982) to carbon-date small fabric samples. [...] The pressure on the ecclesiastic authorities to accept the Turin protocol have almost approached illegality.