Calling plugin controller externally fails with 500 error
So my question is – is there anything special to be aware of when calling plugins from the outside? 


Not particularly.  They're both hitting the same controller endpoint in your plugin, but there are about a million flags/options you can pass into wget to change it's runtime behaviors you might want to play with.

Personally, I stick with using cURL for cronjobs.

Regardless, the behavior you describe sounds like a webserver/Apache crash or segfault.  If they are long-running scripts and you inadvertently triggered them multiple times, maybe you hit some hard resource limits. If that's the case, the underlying error message would be in your web server's error logs for the 500 Internal Server Error.

If it were Craft generated 500 ISEs, then the underlying error message would be in craft/storage/runtime/logs.