The three errors you listed are harmless, but it would be good to address them sometime soon:
1) create custom error pages. If you have cPanel, there is a button "Error Pages" to create the core lines of 400, 401, 403, 404, and /500.shtml. Season with additional HTML code to make them match the look of your site. Those five are the most common -- you can create your own for other errors. When you get an error of some kind (e.g., 404 -- file not found), the server looks for your custom error page. If one doesn't exist, it will fall back to a default handler. It's stupid for it to log an error that it can't find xxx.shtml, but most servers seemed to be configured to do that.
2) create a favicon. This is the 16x16 pixel image that shows up in the browser address bar, tabs, bookmarks, etc. Any "paint" program can create one. It should be "ICON" format and named /favicon.ico. All browsers look for this file and you'll get an error log entry that it can't find it. Do not, I repeat, do not be stupid and create a GIF, JPEG, PNG, or other format image file and rename it to .ico. It won't work.
3) create a /robots.txt file. Initially, it can just be an empty file. Eventually you can put specific commands into it. "Well behaved" search engine spiders read this file to get instructions on what not to go roaming through on your site. If you don't have one (even an empty one), you'll get it logged in your error log.
Creating those files will greatly reduce the junk logged in your error log, enabling you to spot "real" errors more easily.
Now, as for the "blank page" problem, do you mean that when you call up your forum, you get absolutely nothing, just a white screen? That means that some serious error was encountered while processing the files in your forum. There should be some kind of error logged somewhere on your system. There are three places to look:
1) System (site account) control panel error log. If you have cPanel, there is a button labeled "Error Log" (not "Error Pages"). Is there anything listed there?
2) "error_log" file(s) in various directories. If configured to do this, PHP will write error messages to a file (often named "error_log") in the directory where the error occurred. Go into your site control panel's file manager (cPanel > File Manager) and look around. You can also use an FTP program to do this. The error_log file will give useful error messages about what happened (e.g., a syntax error in line ____ of file ____).
3) SMF forum error log (under Admin). If you can't get to your first page to get logged in, you won't be able to look in this error log.
What causes these errors? Mistakes in hand editing of files, wrong permissions on files (some hosts don't permit 777 permissions, for example), a botched mod or theme install, and hack attempts that messed up file changes.