In the Chrome DevTools console, I keep getting error messages from certain places that do not actually affect my application's performance. Is there a way to filter out errors from those sources? (e.g., a YouTube iframe with errors, certain Chrome Extensions, etc.)
Yes, you can. You are able to filter messages from any file source by right-clicking on the file's name and line (something like main.js:15) and selecting Hide messages from *filename*. This will block all messages coming from that file (as is probably self-explanatory given what the button says).
Warning: This will also block messages using console.log() that might harm your debugging process, as well as errors that might come up in the future and be important (which you will now not know about). Use with caution on your own files. It should be harmless with files that aren't yours (again, things like iframes and extensions).
You can reverse the block by going up to the Filter dialog box near the top of the console (to the right of the eye icon) and deleting it. (This will also delete all other filters, so you could just remove one if you needed.) You can also more specifically filter messages using Filter, but for the purposes of the question (blocking messages from a certain file), it does the job the fastest and the best.
For more information, see: https://developers.google.com/web/tools/chrome-devtools/console/reference#filter. This also includes information on the other ways to more specifically filter console messages.