São esses vídeos em Flash? Poderia ser possível se eles estivessem fluindo para o Firefox no Windows XP. Nesse caso, pode haver um problema com as configurações de segurança conectadas ao fluxo de conteúdo de terceiros para a sua máquina. Mais detalhes aqui no site oficial da Macromedia ; esses detalhes parecem estar em jogo:
When you visit a website, the address shown in the browser address bar is usually where most of the website is located. For example, if you visit a fictional website www.[hotel].com, most of the website is located at www.[hotel].com. Sometimes, websites combine content from different sources. For example, www.[hotel].com might display a reservations form in Flash that actually comes from [reservations.hotel].com. The content from the latter website is called third-party content.
Third-party content might try to store information on your computer. In the hotel reservations example, you might be willing to let [reservations.hotel].com store information on your computer, such as data about which hotels you prefer, so that you can make a hotel reservation. However, you might not be willing to let third-party content store information on your computer in other situations. For example, a car-rental company, www.[my-car-rental].com, might have a banner ad on www.[hotel].com, to track your website usage or to record your preferences.
To prohibit all third parties from storing information on your computer, deselect Allow Third-Party Content To Store Data On Your Computer. This option is available only with Flash Player 8 and later. Adobe recommends that you upgrade to the most recent version of Flash Player available.
O que basicamente significa que, se você está tendo problemas, possivelmente permitir que dados de terceiros sejam armazenados em sua máquina localmente resolveria o problema. Se você acessar a página da Macromedia que eu vinculei acima e aqui também —Você verá um painel de controle como este:
Bastamarcaressacaixaaoladode"Permitir que conteúdo Flash de terceiros armazene dados em seu computador". E veja o que acontece.