We will use egrep which accepts a regular expression to grep for multiple strings.
tail -f localhost_access_log.txt | egrep "\" 404|\" 500"
Here our example looks at logs to see if we got 404 or 500 request.
"GET /favicon.ico HTTP/1.1" 404 973 "GET /login.html HTTP/1.1" 500 1230 "GET /favicon.ico HTTP/1.1" 404 973