When I shutdown my computer last night, it gave me this error message. It seems to be working fine but should I be considered?

Attempting to kill init means that something tried to kill PID 1. That's... abnormal outside of a shutdown. But it can be normal during shutdown. So uhh... yeah: if it continues to be a problem then it needs to be reported and fixed by your distribution. What distribution are you using?

I see kernel panics at shutdown most often on Arch-based distros after updating system packages.

It sucks when it happens during shutdown but it's typically not going to cause other problems... except perhaps not automatically booting if you wanted to reboot instead of shutdown.

I'm using the XFCE edition of Linux Mint. The Kernel updated yesterday morning, could that have something to do with it?
- A kernel update, if it's done right, shouldn't cause a panic. But not every distro does updates right.
  
  If you know the old version and the new version then it might be useful to reach out to the Mint community and see if they're aware of issues like that.
  
  https://linuxmint.com/getinvolved.php -> forums or chat might be fruitful to you
I see kernel panics at shutdown most often on Arch-based distros after updating system packages.

When I tried Arch, upgrading kernel would delete the kernel modules of the running kernel --- somewhat unimpressive upgrade process.
This dude kernel panics

I'd reinstall libpcre, looks like it's gotten broken?

The kernel panic should be a direct result of shutdown (which I guess at this point is init/pid1) not finding its dependency and killing itself.

How would I reinstall it? I tried to look it up but I couldn't find anything.
- apt install --reinstall PKG_NAME
  
  Is the command to reinstall a package, replace PKG_NAME with the name of the package you want to reinstall.
  
  You should use apt instead of apt-get. It is newer, more user friendly and supposedly handles dependency resolution better.
- sudo apt-get install --reinstall
  
  https://duckduckgo.com/?q=apt+reinstall+package&t=fpas&ia=qa&iax=qa
  
  Not sure how you searched but I assume you didn't use or know apt? How do you install packages in the first place? Through GUI or Terminal?
  
  EDIT: I assume you use the Linux Mint GUI package manager. I can't find how to do this too, would need to search more detailed but I don't have enough time for this now, need sleep, don't have enough sleep.

Yes this is a kernel panic which occurs when something goes terribly wrong inside the system. This could be anything from broken software to defective hardware. You should observe if this happens regurlarly.

Ok but is there anything notable from this error message, like anything specific that I should be checking out for?
- First line of your picture is a hint for a software issue. I would just google that.

You could look at the package that's mentioned in the first line in Synaptic. The error message says it can't find a file. Fürst thing is do is check if that fike is actually there.

I might be totally wrong, but libpcre sounds like the regex library used by perl. Maybe his perl packages are broken?
- Almost. It's a C library that mimics Perl's regular expression facilities. Fairly common dependency for any number of packages.
Apt says it's installed. Someone said something about reinstalling it but I couldn't find anything online about reinstalling.

Your libpcre seems broken. Reinstall the package that contains this file.

I did that yesterday and it might have fixed it because I didn't have the issue but I did try multiple things yesterday, so I'm not sure.

You seem to have removed libpcre2 library. Try to reinstall it using your package manager.

Synaptic Package Manager states that there are several versions of libpcre2 installed, which one should I try to reinstall?
- It seems the 'libpcre2-8-0' is installed and the first line in your first screenshot complains about that one. If it is not solved, run 'ldd /sbin/shutdown' and you should see where it expects libpcre2 to be. 'ls' that path and see if it is there. If it is, is it on another mount than root that gets unmounted too early or something? If it is not there, try reintalling the package, or see where the package puts that library file. If it is in the wrong place, use 'ln -s' to create a symbolic link to where shutdown expects it.

In addition to the other things mentioned, check the health of your drive. This could be a symptom of corruption.