Check that your mask has a backstrap fitted. This is a piece of elastic approximately 2 inches wide attached across the back of the mask to prevent it falling off during fencing.
The bib (the padded front piece of the mask that protects the throat) should be sewn on firmly with no holes that would allow a blade to penetrate.
The mesh of the mask (the face) should not be soft enough to push in using your thumbs, nor should it have any rust.
It is important to try and obtain the correct size mask to wear while fencing. It’s very difficult to concentrate on fencing while your head is rattling around inside a mask 2 sizes too big for you!
Masks come in different weights (measured in Newtons of force) offering levels of protection. 600N is the current minimum for club use. When buying new, get an 1600N mask.