When writing any kind of log files you can of course show them on the console by opening them in any kind of editor be it vim, less or just a simple cat. But you need to run the command every single time you run a process that writes something into the file.

A better way is to use tail with the -f option. With it you jump into the file and stay there. Any changes into the file will be shown immediately:

$ tail -f /tmp/error.log