What should I do about an Old Catholic Church in my city? It makes several claims on its website about its sacraments being valid.
Because its bishops had been validly ordained, they retained the ability to ordain other bishops and priests.
This was confirmed on January 3, 1987, by the Congregation for the Doctrine of the Faith (Prot. no. 795/68):
Among the churches which are in the same situation as the oriental churches named in can. 844 § 3 we include the Old Catholic churches in Europe and the Polish National Church in the United States of America.
The Catholic Church has recognized the sacraments of the Old Catholic Church as valid and in the same category as the sacraments of the Eastern Orthodox Churches. However, the Old Catholic Church in more recent times has begun ordaining women. Since such ordinations are invalid, the Catholic Church cannot recognize any sacraments (other than baptism) as valid that a female priest performs.
This issue also presents problems when it comes to valid lines of apostolic succession. A female bishop can impart ordination to neither priests nor bishops, thus rendering their ordination and sacraments also invalid (except for baptisms). As of now, I am unaware that the Old Catholic Church has ordained any female bishops, and thus its line of apostolic succession appears to still be valid.
Even though the sacraments of these churches are valid (when performed by a validly ordained priest), they are still illicit, and therefore Catholics should avoid them outside a danger-of-death situation.