Okay, great news! The reason installer is failing is because it cannot add the watcher/logger to crontab. This is not a huge problem at all. You can manually add it. The reason it is failing is because you have PHP Safe mode on (again, this is not a problem).
Even if you do not add the watcher to crontab, the web app will work.
To add the watcher to the crontab do the following:
* * * * * cd /volume1/web/sprinklers; php /volume1/web/sprinklers/watcher.php >/dev/null 2>&1
As for the final error: I cannot determine what line 419 in main.php is because I have pushed several updates to the code recently. If you could copy paste line 419 from main.php I could further debug the cause of that (or update to the latest version out now, 18 minutes old, and paste any new errors).
As a final summary, based on your Safe Mode error I suspect everything up until then went fine which means your config.php, user files, and log files should be created and saved properly. From here, update to the latest, add your watcher to cron manually like instructed above and give me any new errors you may receive.
Edit: I updated the installer to catch crontab failure and show the proper error message. It will also take you to the login screen after this error since it is non-critical.