>I have my web.config error setting at "Remote Only" so the users don't see any .NET errors they may receive. Now, I need to write the error to an error log, so if users do get errors, I can research and debug. Is the .NET EventLog component the tool I should be using to go about this?

Have you taken a look at the Logging Application Block from Microsoft?:

http://msdn.microsoft.com/library/default.asp?url=/library/en-us/dnpag/html/Logging.asp?frame=tru