If the woman involved in an invalid “get” has children by another man, the child is a putative mamzer. The reason for saying “putative” is that in practice most batei dinim tend to “bend over backwards” to avoid deciding that someone is a mamzer, so unless a “get” is clearly invalid by at opinons, the likelihood was/is/will be that the child will eventually be held to be a non-mamzer (either by validating the “get” or otherwise, such as by finding the marriage to have been invalid). In this area the “theory” as to what halacha is tends to vary from what most rabbanim end up deciding in actual cases involving the children of the woman with a dubious “get.”
If you don’t believe, do an empirical study of shaiolohs and tseuvahs.