Instead of opening the entire file, you could read the last [insert number here] lines with the "tail" command:
tail -n 1000 /var/log/messages
This will print the last 1000 lines of the messages log file to your screen.
tail -f /var/log/messages
This continuously prints new lines to the messages log file.
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There's a bunch of webserver log analyzers, I use Sawmill which tends to do the job nicely. For the error logs, just browse through em and see if you find anything noteworthy, if you do, then dig deeper to see if it's a server problem or if someones poking around where they shouldnt