What that means is if you've got software on your Linux box that was compiled against, say version 0.9 of the OpenSSL libraries, but then your next patch pull from the Linux Distribution updates the OpenSSL libraries to 1.0, which breaks your software.
If you're using a mainstream Linux distro then it handles all of that for you. It's no worse than using Windows Update, which has had its howlers over the years. Just occasionally I'll have a hiccup when doing an update, but that's usually because I'm trying to do an update that is still being rolled out to the various mirror sites and it resolves itself (i.e. works) within a few hours.
I would say that Linux Mint is a perfectly adequate replacement for XP if all you need to do is web browsing, read email and do a bit of word processing. It will put in a decent performance on old hardware that can't handle newer Windows versions, too. There's the added advantage of not needing all that anti-virus software slowing the machine down, too.