Here are some possible reasons for unexpected behavior.
In most cases, debug mode should be off, but if you're experiencing problems, the first thing you should do is turn on DEBUG in Admin -> Settings. This will display any errors on the screen. You might also check error_log.php in Admin -> Maintenance. If for any reason you can't enable debug mode in Admin, you can do it in the database using phpMyAdmin. Find the settings table and set DEBUG to true.
Go to /hotaru_settings.php and make sure the BASEURL ends with "/".
If you have a .htaccess file on your web server in Hotaru's directory, turn off FRIENDLY URLS in Admin -> Settings then remove the .htaccess file for now.
Try a hard refresh, CTRL+F5, to make sure you're looking at a fresh page.
If the problem is CSS or JavaScript related, go to Admin -> Maintenance, clear the css/js cache, return to the page you were having a problem on and do a hard refresh. If you prefer, you can disable the css/js cache in Admin -> Settings.
Clearing the cache when you encounter problems remedies most problems. Just go to Admin -> Maintenance and click "Clear database cache" to instantly delete all the cached files.
You can disable or change the duration of the database cache in Admin - > Settings.
Depending on the order you install certain plugins, it's possible the resulting behavior might differ. Take for example the navigation bar. The SB Base plugin adds "Top Stories" and "Latest" to the navigation bar and the Submit plugin adds "Submit a Story". The order those links appear in the navigation bar depends on the order you install those plugins. While that particular example won't break your website, more complicated plugin functions could cause unexpected results if fired in the wrong order. See Installing Your First Plugins.
The solution is simply to go to Admin -> Plugin Management and click the up and down arrows to change the order the actions are triggered in.
If you're getting 403 Permission Denied or similar errors, it might be because of your server's mod_security settings. Explain the problem to your web host and ask them if mod_security has flagged anything lately.
As stated on the download page, Hotaru CMS has been tested using PHP 5.2.6 ~ 5.3.1, MySQL 5.0 and phpMyAdmin 2.11.6 ~ 3.2.5. Anything lower is likely to cause problems.