Being a Firefox user, you might face an issue that some videos do not play for you when you don't have Adobe Flash installed. Luckily for us, Firefox is an HTML5 compatible browser. Instead of installing Flash, you can tweak the browser and make YouTube work for you without Flash. To get it working, you need to enable the Media Source Extensions feature which is disabled by default.
Adobe's Flash Player is something that you need to update constantly. Just 2 days ago, Adobe released an emergency update for Flash Player to fix a critical remote code execution vulnerability that hackers on the web are actively exploiting. However, even if Flash Player's installer has automatic update checking and the ability to update automatically, you may want to download the full Flash Player installer to update multiple machines quickly. Here are direct download links for it.